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Cayley's Matrix Notation


Checking whether or not a node has been previously definedMath notation and FontsDouble vertical bar notation“Where” notation in definitionNotation for multivariate normalWhich “bold” style is recommended for matrix notation?Math notation in LaTeX?Physics notationPercent notationSummation notation with an incrementUsing printeranswers environment, how to print solutions in the box without the title “Solutions”













3















Cayley used the following notation in his original paper
A Memoir on the Theory of Matrices 1



enter image description here



My attempt to reproduce the notation is shown below:



documentclassarticle
usepackageamsmath,amssymb,graphicx
begindocument
scalebox2.5parbox0.3textwidth$$
renewcommandarraystretch0setlengtharraycolsep0pt
(mathrmX, mathrmY, mathrmZ)=lower10pthbox$beginarrayr@c@,mkern10muc @,mkern10muc@,mkern10muc l
( &a &b & c & )\
lvert& a' &b' & c' &rvert\
lvert& a'' & b'' & c'' & rvert\
endarray$mkern-6mu(x,y,z),
$$
enddocument


As you will observe the delimiters need to be improved. Any suggestions?










share|improve this question






















  • is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

    – David Carlisle
    2 hours ago











  • more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

    – David Carlisle
    2 hours ago











  • @DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

    – Yiannis Lazarides
    2 hours ago















3















Cayley used the following notation in his original paper
A Memoir on the Theory of Matrices 1



enter image description here



My attempt to reproduce the notation is shown below:



documentclassarticle
usepackageamsmath,amssymb,graphicx
begindocument
scalebox2.5parbox0.3textwidth$$
renewcommandarraystretch0setlengtharraycolsep0pt
(mathrmX, mathrmY, mathrmZ)=lower10pthbox$beginarrayr@c@,mkern10muc @,mkern10muc@,mkern10muc l
( &a &b & c & )\
lvert& a' &b' & c' &rvert\
lvert& a'' & b'' & c'' & rvert\
endarray$mkern-6mu(x,y,z),
$$
enddocument


As you will observe the delimiters need to be improved. Any suggestions?










share|improve this question






















  • is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

    – David Carlisle
    2 hours ago











  • more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

    – David Carlisle
    2 hours ago











  • @DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

    – Yiannis Lazarides
    2 hours ago













3












3








3


2






Cayley used the following notation in his original paper
A Memoir on the Theory of Matrices 1



enter image description here



My attempt to reproduce the notation is shown below:



documentclassarticle
usepackageamsmath,amssymb,graphicx
begindocument
scalebox2.5parbox0.3textwidth$$
renewcommandarraystretch0setlengtharraycolsep0pt
(mathrmX, mathrmY, mathrmZ)=lower10pthbox$beginarrayr@c@,mkern10muc @,mkern10muc@,mkern10muc l
( &a &b & c & )\
lvert& a' &b' & c' &rvert\
lvert& a'' & b'' & c'' & rvert\
endarray$mkern-6mu(x,y,z),
$$
enddocument


As you will observe the delimiters need to be improved. Any suggestions?










share|improve this question














Cayley used the following notation in his original paper
A Memoir on the Theory of Matrices 1



enter image description here



My attempt to reproduce the notation is shown below:



documentclassarticle
usepackageamsmath,amssymb,graphicx
begindocument
scalebox2.5parbox0.3textwidth$$
renewcommandarraystretch0setlengtharraycolsep0pt
(mathrmX, mathrmY, mathrmZ)=lower10pthbox$beginarrayr@c@,mkern10muc @,mkern10muc@,mkern10muc l
( &a &b & c & )\
lvert& a' &b' & c' &rvert\
lvert& a'' & b'' & c'' & rvert\
endarray$mkern-6mu(x,y,z),
$$
enddocument


As you will observe the delimiters need to be improved. Any suggestions?







math-mode






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 2 hours ago









Yiannis LazaridesYiannis Lazarides

93k21235516




93k21235516












  • is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

    – David Carlisle
    2 hours ago











  • more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

    – David Carlisle
    2 hours ago











  • @DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

    – Yiannis Lazarides
    2 hours ago

















  • is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

    – David Carlisle
    2 hours ago











  • more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

    – David Carlisle
    2 hours ago











  • @DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

    – Yiannis Lazarides
    2 hours ago
















is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

– David Carlisle
2 hours ago





is it just my eyes or am I right in thinking that on its own the () are symmetric pair but the overlapping )( symbol is using thinner more rounded )( to get more of an overlap so not using the matching parens for the outer borders of the matrices....

– David Carlisle
2 hours ago













more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

– David Carlisle
2 hours ago





more $(1,2,3between 4,5,6)$ than $(1,2,3)!( 4,5,6)$

– David Carlisle
2 hours ago













@DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

– Yiannis Lazarides
2 hours ago





@DavidCarlisle No it is the same thickness. There is a link to the Royal Society paper jstor.org/stable/pdf/108649.pdf

– Yiannis Lazarides
2 hours ago










4 Answers
4






active

oldest

votes


















1














Here is an approximation, with basic commands:



documentclassarticle
usepackageamsmath,amssymb,graphicx

begindocument

[ beginarrayc@ccc@c
(mkern 4.2mu & a &b & c &mkern 4.2mu)\[-0.31ex]
vline & a' &b' & c' & vline \
vline & a'' &b'' & c''& vline
endarray ]%

enddocument


enter image description here






share|improve this answer






























    1














    My proposal:



    documentclassarticle
    usepackageamsmath,amssymb,graphicx

    DeclareMathSymbolAmathalphaoperators`A
    DeclareMathSymbolBmathalphaoperators`B
    DeclareMathSymbolCmathalphaoperators`C
    DeclareMathSymbolDmathalphaoperators`D
    DeclareMathSymbolEmathalphaoperators`E
    DeclareMathSymbolFmathalphaoperators`F
    DeclareMathSymbolGmathalphaoperators`G
    DeclareMathSymbolHmathalphaoperators`H
    DeclareMathSymbolImathalphaoperators`I
    DeclareMathSymbolJmathalphaoperators`J
    DeclareMathSymbolKmathalphaoperators`K
    DeclareMathSymbolLmathalphaoperators`L
    DeclareMathSymbolMmathalphaoperators`M
    DeclareMathSymbolNmathalphaoperators`N
    DeclareMathSymbolOmathalphaoperators`O
    DeclareMathSymbolPmathalphaoperators`P
    DeclareMathSymbolQmathalphaoperators`Q
    DeclareMathSymbolRmathalphaoperators`R
    DeclareMathSymbolSmathalphaoperators`S
    DeclareMathSymbolTmathalphaoperators`T
    DeclareMathSymbolUmathalphaoperators`U
    DeclareMathSymbolVmathalphaoperators`V
    DeclareMathSymbolWmathalphaoperators`W
    DeclareMathSymbolXmathalphaoperators`X
    DeclareMathSymbolYmathalphaoperators`Y
    DeclareMathSymbolZmathalphaoperators`Z


    newsaveboxcayleybox
    newlengthcayleyheight
    newenvironmentcayleymatrix[1]
    beginlrboxcayleybox
    $beginarray@enspacel*numexpr#1-1@,enspacel@enspace
    endarray$endlrbox%
    setlengthcayleyheightdimexprhtcayleybox+dpcayleybox%
    kern-0.8pt
    vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
    raiseboxdimexprhtstrutbox-htcayleyboxuseboxcayleybox%
    vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
    kern-0.8pt

    newcommandbykern-0.4ptbetweenkern-0.4pt

    thinmuskip=6mu
    medmuskip=0mu
    thickmuskip=0mu

    begindocument

    [ % page 17
    (X,Y,Z)=
    (begincayleymatrix3
    a & b & c \
    a' & b' & c' \
    a'' & b'' & c''
    endcayleymatrix
    by x,y,z)
    ]

    [ % page 32
    (begincayleymatrix2 a & c \ b & d endcayleymatrix by
    begincayleymatrix2 a & b \ c & d endcayleymatrix by
    begincayleymatrix2 a & c \ b & d endcayleymatrix by
    begincayleymatrix2 a & b \ c & d endcayleymatrix )
    =
    bigl(
    (begincayleymatrix2 a & c \ b & d endcayleymatrixby
    begincayleymatrix2 a & b \ c & d endcayleymatrix)
    bigr)^2
    ]

    enddocument


    enter image description here






    share|improve this answer






























      1














      Extending Bernard's idea slightly:



      enter image description here



      ...but not quite up to the standards of egreg's nice solution:)



      documentclassarticle
      usepackagearray
      newcountercayley
      newcolumntypeL>stepcountercayley%
      ifnumvaluecayley=1raisebox-0.4ex(kern0.5exelsevlinefic@
      newcolumntypeR@c<spaceifnumvaluecayley=1kern0.5exraisebox-0.4ex)elsevlinefi
      newenvironmentcayley[1][3]setcountercayley0arrayL*#1cRendarray

      begindocument

      [
      begincayley
      &a & b & c &\
      &a' & b' & c' &\
      &a''& b''& c''&\
      endcayley
      qquad
      begincayley[4]
      &a & b & c & d &\
      &a' & b' & c' & d' &\
      &a''& b''& c''& d''&\
      endcayley
      ]

      enddocument





      share|improve this answer






























        0














        A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



        documentclassarticle
        usepackagetikz
        makeatletter% https://tex.stackexchange.com/a/85531/121799
        longdefifnodedefined#1#2#3%
        @ifundefinedpgf@sh@ns@#1#3#2%

        makeatother
        newcounterCM
        usetikzlibrarymatrix
        newcommandCayleyMatrix[2][]stepcounterCM%
        begintikzpicture[baseline=(mat-numbervalueCM-1-1.base),inner sep=2pt,#1]
        matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalueCM)
        #2
        ;
        ifnodedefinedmat-numbervalueCM-2-1-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
        (mat-numbervalueCM.south west-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
        (mat-numbervalueCM.south west
        endtikzpicture
        begindocument
        [CayleyMatrix
        X &Y & Z \
        =CayleyMatrix
        a &b & c \
        a' &b' & c' \
        a'' & b'' & c'' \
        !!CayleyMatrix
        x &y & z \
        ]
        enddocument


        enter image description here






        share|improve this answer























          Your Answer








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          4 Answers
          4






          active

          oldest

          votes








          4 Answers
          4






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          1














          Here is an approximation, with basic commands:



          documentclassarticle
          usepackageamsmath,amssymb,graphicx

          begindocument

          [ beginarrayc@ccc@c
          (mkern 4.2mu & a &b & c &mkern 4.2mu)\[-0.31ex]
          vline & a' &b' & c' & vline \
          vline & a'' &b'' & c''& vline
          endarray ]%

          enddocument


          enter image description here






          share|improve this answer



























            1














            Here is an approximation, with basic commands:



            documentclassarticle
            usepackageamsmath,amssymb,graphicx

            begindocument

            [ beginarrayc@ccc@c
            (mkern 4.2mu & a &b & c &mkern 4.2mu)\[-0.31ex]
            vline & a' &b' & c' & vline \
            vline & a'' &b'' & c''& vline
            endarray ]%

            enddocument


            enter image description here






            share|improve this answer

























              1












              1








              1







              Here is an approximation, with basic commands:



              documentclassarticle
              usepackageamsmath,amssymb,graphicx

              begindocument

              [ beginarrayc@ccc@c
              (mkern 4.2mu & a &b & c &mkern 4.2mu)\[-0.31ex]
              vline & a' &b' & c' & vline \
              vline & a'' &b'' & c''& vline
              endarray ]%

              enddocument


              enter image description here






              share|improve this answer













              Here is an approximation, with basic commands:



              documentclassarticle
              usepackageamsmath,amssymb,graphicx

              begindocument

              [ beginarrayc@ccc@c
              (mkern 4.2mu & a &b & c &mkern 4.2mu)\[-0.31ex]
              vline & a' &b' & c' & vline \
              vline & a'' &b'' & c''& vline
              endarray ]%

              enddocument


              enter image description here







              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered 1 hour ago









              BernardBernard

              177k779211




              177k779211





















                  1














                  My proposal:



                  documentclassarticle
                  usepackageamsmath,amssymb,graphicx

                  DeclareMathSymbolAmathalphaoperators`A
                  DeclareMathSymbolBmathalphaoperators`B
                  DeclareMathSymbolCmathalphaoperators`C
                  DeclareMathSymbolDmathalphaoperators`D
                  DeclareMathSymbolEmathalphaoperators`E
                  DeclareMathSymbolFmathalphaoperators`F
                  DeclareMathSymbolGmathalphaoperators`G
                  DeclareMathSymbolHmathalphaoperators`H
                  DeclareMathSymbolImathalphaoperators`I
                  DeclareMathSymbolJmathalphaoperators`J
                  DeclareMathSymbolKmathalphaoperators`K
                  DeclareMathSymbolLmathalphaoperators`L
                  DeclareMathSymbolMmathalphaoperators`M
                  DeclareMathSymbolNmathalphaoperators`N
                  DeclareMathSymbolOmathalphaoperators`O
                  DeclareMathSymbolPmathalphaoperators`P
                  DeclareMathSymbolQmathalphaoperators`Q
                  DeclareMathSymbolRmathalphaoperators`R
                  DeclareMathSymbolSmathalphaoperators`S
                  DeclareMathSymbolTmathalphaoperators`T
                  DeclareMathSymbolUmathalphaoperators`U
                  DeclareMathSymbolVmathalphaoperators`V
                  DeclareMathSymbolWmathalphaoperators`W
                  DeclareMathSymbolXmathalphaoperators`X
                  DeclareMathSymbolYmathalphaoperators`Y
                  DeclareMathSymbolZmathalphaoperators`Z


                  newsaveboxcayleybox
                  newlengthcayleyheight
                  newenvironmentcayleymatrix[1]
                  beginlrboxcayleybox
                  $beginarray@enspacel*numexpr#1-1@,enspacel@enspace
                  endarray$endlrbox%
                  setlengthcayleyheightdimexprhtcayleybox+dpcayleybox%
                  kern-0.8pt
                  vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
                  raiseboxdimexprhtstrutbox-htcayleyboxuseboxcayleybox%
                  vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
                  kern-0.8pt

                  newcommandbykern-0.4ptbetweenkern-0.4pt

                  thinmuskip=6mu
                  medmuskip=0mu
                  thickmuskip=0mu

                  begindocument

                  [ % page 17
                  (X,Y,Z)=
                  (begincayleymatrix3
                  a & b & c \
                  a' & b' & c' \
                  a'' & b'' & c''
                  endcayleymatrix
                  by x,y,z)
                  ]

                  [ % page 32
                  (begincayleymatrix2 a & c \ b & d endcayleymatrix by
                  begincayleymatrix2 a & b \ c & d endcayleymatrix by
                  begincayleymatrix2 a & c \ b & d endcayleymatrix by
                  begincayleymatrix2 a & b \ c & d endcayleymatrix )
                  =
                  bigl(
                  (begincayleymatrix2 a & c \ b & d endcayleymatrixby
                  begincayleymatrix2 a & b \ c & d endcayleymatrix)
                  bigr)^2
                  ]

                  enddocument


                  enter image description here






                  share|improve this answer



























                    1














                    My proposal:



                    documentclassarticle
                    usepackageamsmath,amssymb,graphicx

                    DeclareMathSymbolAmathalphaoperators`A
                    DeclareMathSymbolBmathalphaoperators`B
                    DeclareMathSymbolCmathalphaoperators`C
                    DeclareMathSymbolDmathalphaoperators`D
                    DeclareMathSymbolEmathalphaoperators`E
                    DeclareMathSymbolFmathalphaoperators`F
                    DeclareMathSymbolGmathalphaoperators`G
                    DeclareMathSymbolHmathalphaoperators`H
                    DeclareMathSymbolImathalphaoperators`I
                    DeclareMathSymbolJmathalphaoperators`J
                    DeclareMathSymbolKmathalphaoperators`K
                    DeclareMathSymbolLmathalphaoperators`L
                    DeclareMathSymbolMmathalphaoperators`M
                    DeclareMathSymbolNmathalphaoperators`N
                    DeclareMathSymbolOmathalphaoperators`O
                    DeclareMathSymbolPmathalphaoperators`P
                    DeclareMathSymbolQmathalphaoperators`Q
                    DeclareMathSymbolRmathalphaoperators`R
                    DeclareMathSymbolSmathalphaoperators`S
                    DeclareMathSymbolTmathalphaoperators`T
                    DeclareMathSymbolUmathalphaoperators`U
                    DeclareMathSymbolVmathalphaoperators`V
                    DeclareMathSymbolWmathalphaoperators`W
                    DeclareMathSymbolXmathalphaoperators`X
                    DeclareMathSymbolYmathalphaoperators`Y
                    DeclareMathSymbolZmathalphaoperators`Z


                    newsaveboxcayleybox
                    newlengthcayleyheight
                    newenvironmentcayleymatrix[1]
                    beginlrboxcayleybox
                    $beginarray@enspacel*numexpr#1-1@,enspacel@enspace
                    endarray$endlrbox%
                    setlengthcayleyheightdimexprhtcayleybox+dpcayleybox%
                    kern-0.8pt
                    vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
                    raiseboxdimexprhtstrutbox-htcayleyboxuseboxcayleybox%
                    vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
                    kern-0.8pt

                    newcommandbykern-0.4ptbetweenkern-0.4pt

                    thinmuskip=6mu
                    medmuskip=0mu
                    thickmuskip=0mu

                    begindocument

                    [ % page 17
                    (X,Y,Z)=
                    (begincayleymatrix3
                    a & b & c \
                    a' & b' & c' \
                    a'' & b'' & c''
                    endcayleymatrix
                    by x,y,z)
                    ]

                    [ % page 32
                    (begincayleymatrix2 a & c \ b & d endcayleymatrix by
                    begincayleymatrix2 a & b \ c & d endcayleymatrix by
                    begincayleymatrix2 a & c \ b & d endcayleymatrix by
                    begincayleymatrix2 a & b \ c & d endcayleymatrix )
                    =
                    bigl(
                    (begincayleymatrix2 a & c \ b & d endcayleymatrixby
                    begincayleymatrix2 a & b \ c & d endcayleymatrix)
                    bigr)^2
                    ]

                    enddocument


                    enter image description here






                    share|improve this answer

























                      1












                      1








                      1







                      My proposal:



                      documentclassarticle
                      usepackageamsmath,amssymb,graphicx

                      DeclareMathSymbolAmathalphaoperators`A
                      DeclareMathSymbolBmathalphaoperators`B
                      DeclareMathSymbolCmathalphaoperators`C
                      DeclareMathSymbolDmathalphaoperators`D
                      DeclareMathSymbolEmathalphaoperators`E
                      DeclareMathSymbolFmathalphaoperators`F
                      DeclareMathSymbolGmathalphaoperators`G
                      DeclareMathSymbolHmathalphaoperators`H
                      DeclareMathSymbolImathalphaoperators`I
                      DeclareMathSymbolJmathalphaoperators`J
                      DeclareMathSymbolKmathalphaoperators`K
                      DeclareMathSymbolLmathalphaoperators`L
                      DeclareMathSymbolMmathalphaoperators`M
                      DeclareMathSymbolNmathalphaoperators`N
                      DeclareMathSymbolOmathalphaoperators`O
                      DeclareMathSymbolPmathalphaoperators`P
                      DeclareMathSymbolQmathalphaoperators`Q
                      DeclareMathSymbolRmathalphaoperators`R
                      DeclareMathSymbolSmathalphaoperators`S
                      DeclareMathSymbolTmathalphaoperators`T
                      DeclareMathSymbolUmathalphaoperators`U
                      DeclareMathSymbolVmathalphaoperators`V
                      DeclareMathSymbolWmathalphaoperators`W
                      DeclareMathSymbolXmathalphaoperators`X
                      DeclareMathSymbolYmathalphaoperators`Y
                      DeclareMathSymbolZmathalphaoperators`Z


                      newsaveboxcayleybox
                      newlengthcayleyheight
                      newenvironmentcayleymatrix[1]
                      beginlrboxcayleybox
                      $beginarray@enspacel*numexpr#1-1@,enspacel@enspace
                      endarray$endlrbox%
                      setlengthcayleyheightdimexprhtcayleybox+dpcayleybox%
                      kern-0.8pt
                      vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
                      raiseboxdimexprhtstrutbox-htcayleyboxuseboxcayleybox%
                      vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
                      kern-0.8pt

                      newcommandbykern-0.4ptbetweenkern-0.4pt

                      thinmuskip=6mu
                      medmuskip=0mu
                      thickmuskip=0mu

                      begindocument

                      [ % page 17
                      (X,Y,Z)=
                      (begincayleymatrix3
                      a & b & c \
                      a' & b' & c' \
                      a'' & b'' & c''
                      endcayleymatrix
                      by x,y,z)
                      ]

                      [ % page 32
                      (begincayleymatrix2 a & c \ b & d endcayleymatrix by
                      begincayleymatrix2 a & b \ c & d endcayleymatrix by
                      begincayleymatrix2 a & c \ b & d endcayleymatrix by
                      begincayleymatrix2 a & b \ c & d endcayleymatrix )
                      =
                      bigl(
                      (begincayleymatrix2 a & c \ b & d endcayleymatrixby
                      begincayleymatrix2 a & b \ c & d endcayleymatrix)
                      bigr)^2
                      ]

                      enddocument


                      enter image description here






                      share|improve this answer













                      My proposal:



                      documentclassarticle
                      usepackageamsmath,amssymb,graphicx

                      DeclareMathSymbolAmathalphaoperators`A
                      DeclareMathSymbolBmathalphaoperators`B
                      DeclareMathSymbolCmathalphaoperators`C
                      DeclareMathSymbolDmathalphaoperators`D
                      DeclareMathSymbolEmathalphaoperators`E
                      DeclareMathSymbolFmathalphaoperators`F
                      DeclareMathSymbolGmathalphaoperators`G
                      DeclareMathSymbolHmathalphaoperators`H
                      DeclareMathSymbolImathalphaoperators`I
                      DeclareMathSymbolJmathalphaoperators`J
                      DeclareMathSymbolKmathalphaoperators`K
                      DeclareMathSymbolLmathalphaoperators`L
                      DeclareMathSymbolMmathalphaoperators`M
                      DeclareMathSymbolNmathalphaoperators`N
                      DeclareMathSymbolOmathalphaoperators`O
                      DeclareMathSymbolPmathalphaoperators`P
                      DeclareMathSymbolQmathalphaoperators`Q
                      DeclareMathSymbolRmathalphaoperators`R
                      DeclareMathSymbolSmathalphaoperators`S
                      DeclareMathSymbolTmathalphaoperators`T
                      DeclareMathSymbolUmathalphaoperators`U
                      DeclareMathSymbolVmathalphaoperators`V
                      DeclareMathSymbolWmathalphaoperators`W
                      DeclareMathSymbolXmathalphaoperators`X
                      DeclareMathSymbolYmathalphaoperators`Y
                      DeclareMathSymbolZmathalphaoperators`Z


                      newsaveboxcayleybox
                      newlengthcayleyheight
                      newenvironmentcayleymatrix[1]
                      beginlrboxcayleybox
                      $beginarray@enspacel*numexpr#1-1@,enspacel@enspace
                      endarray$endlrbox%
                      setlengthcayleyheightdimexprhtcayleybox+dpcayleybox%
                      kern-0.8pt
                      vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
                      raiseboxdimexprhtstrutbox-htcayleyboxuseboxcayleybox%
                      vtop to cayleyheighthboxvphantom$between$leadersvrulevfill%
                      kern-0.8pt

                      newcommandbykern-0.4ptbetweenkern-0.4pt

                      thinmuskip=6mu
                      medmuskip=0mu
                      thickmuskip=0mu

                      begindocument

                      [ % page 17
                      (X,Y,Z)=
                      (begincayleymatrix3
                      a & b & c \
                      a' & b' & c' \
                      a'' & b'' & c''
                      endcayleymatrix
                      by x,y,z)
                      ]

                      [ % page 32
                      (begincayleymatrix2 a & c \ b & d endcayleymatrix by
                      begincayleymatrix2 a & b \ c & d endcayleymatrix by
                      begincayleymatrix2 a & c \ b & d endcayleymatrix by
                      begincayleymatrix2 a & b \ c & d endcayleymatrix )
                      =
                      bigl(
                      (begincayleymatrix2 a & c \ b & d endcayleymatrixby
                      begincayleymatrix2 a & b \ c & d endcayleymatrix)
                      bigr)^2
                      ]

                      enddocument


                      enter image description here







                      share|improve this answer












                      share|improve this answer



                      share|improve this answer










                      answered 56 mins ago









                      egregegreg

                      737k8919363264




                      737k8919363264





















                          1














                          Extending Bernard's idea slightly:



                          enter image description here



                          ...but not quite up to the standards of egreg's nice solution:)



                          documentclassarticle
                          usepackagearray
                          newcountercayley
                          newcolumntypeL>stepcountercayley%
                          ifnumvaluecayley=1raisebox-0.4ex(kern0.5exelsevlinefic@
                          newcolumntypeR@c<spaceifnumvaluecayley=1kern0.5exraisebox-0.4ex)elsevlinefi
                          newenvironmentcayley[1][3]setcountercayley0arrayL*#1cRendarray

                          begindocument

                          [
                          begincayley
                          &a & b & c &\
                          &a' & b' & c' &\
                          &a''& b''& c''&\
                          endcayley
                          qquad
                          begincayley[4]
                          &a & b & c & d &\
                          &a' & b' & c' & d' &\
                          &a''& b''& c''& d''&\
                          endcayley
                          ]

                          enddocument





                          share|improve this answer



























                            1














                            Extending Bernard's idea slightly:



                            enter image description here



                            ...but not quite up to the standards of egreg's nice solution:)



                            documentclassarticle
                            usepackagearray
                            newcountercayley
                            newcolumntypeL>stepcountercayley%
                            ifnumvaluecayley=1raisebox-0.4ex(kern0.5exelsevlinefic@
                            newcolumntypeR@c<spaceifnumvaluecayley=1kern0.5exraisebox-0.4ex)elsevlinefi
                            newenvironmentcayley[1][3]setcountercayley0arrayL*#1cRendarray

                            begindocument

                            [
                            begincayley
                            &a & b & c &\
                            &a' & b' & c' &\
                            &a''& b''& c''&\
                            endcayley
                            qquad
                            begincayley[4]
                            &a & b & c & d &\
                            &a' & b' & c' & d' &\
                            &a''& b''& c''& d''&\
                            endcayley
                            ]

                            enddocument





                            share|improve this answer

























                              1












                              1








                              1







                              Extending Bernard's idea slightly:



                              enter image description here



                              ...but not quite up to the standards of egreg's nice solution:)



                              documentclassarticle
                              usepackagearray
                              newcountercayley
                              newcolumntypeL>stepcountercayley%
                              ifnumvaluecayley=1raisebox-0.4ex(kern0.5exelsevlinefic@
                              newcolumntypeR@c<spaceifnumvaluecayley=1kern0.5exraisebox-0.4ex)elsevlinefi
                              newenvironmentcayley[1][3]setcountercayley0arrayL*#1cRendarray

                              begindocument

                              [
                              begincayley
                              &a & b & c &\
                              &a' & b' & c' &\
                              &a''& b''& c''&\
                              endcayley
                              qquad
                              begincayley[4]
                              &a & b & c & d &\
                              &a' & b' & c' & d' &\
                              &a''& b''& c''& d''&\
                              endcayley
                              ]

                              enddocument





                              share|improve this answer













                              Extending Bernard's idea slightly:



                              enter image description here



                              ...but not quite up to the standards of egreg's nice solution:)



                              documentclassarticle
                              usepackagearray
                              newcountercayley
                              newcolumntypeL>stepcountercayley%
                              ifnumvaluecayley=1raisebox-0.4ex(kern0.5exelsevlinefic@
                              newcolumntypeR@c<spaceifnumvaluecayley=1kern0.5exraisebox-0.4ex)elsevlinefi
                              newenvironmentcayley[1][3]setcountercayley0arrayL*#1cRendarray

                              begindocument

                              [
                              begincayley
                              &a & b & c &\
                              &a' & b' & c' &\
                              &a''& b''& c''&\
                              endcayley
                              qquad
                              begincayley[4]
                              &a & b & c & d &\
                              &a' & b' & c' & d' &\
                              &a''& b''& c''& d''&\
                              endcayley
                              ]

                              enddocument






                              share|improve this answer












                              share|improve this answer



                              share|improve this answer










                              answered 29 mins ago









                              AndrewAndrew

                              31.4k34483




                              31.4k34483





















                                  0














                                  A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



                                  documentclassarticle
                                  usepackagetikz
                                  makeatletter% https://tex.stackexchange.com/a/85531/121799
                                  longdefifnodedefined#1#2#3%
                                  @ifundefinedpgf@sh@ns@#1#3#2%

                                  makeatother
                                  newcounterCM
                                  usetikzlibrarymatrix
                                  newcommandCayleyMatrix[2][]stepcounterCM%
                                  begintikzpicture[baseline=(mat-numbervalueCM-1-1.base),inner sep=2pt,#1]
                                  matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalueCM)
                                  #2
                                  ;
                                  ifnodedefinedmat-numbervalueCM-2-1-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
                                  (mat-numbervalueCM.south west-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
                                  (mat-numbervalueCM.south west
                                  endtikzpicture
                                  begindocument
                                  [CayleyMatrix
                                  X &Y & Z \
                                  =CayleyMatrix
                                  a &b & c \
                                  a' &b' & c' \
                                  a'' & b'' & c'' \
                                  !!CayleyMatrix
                                  x &y & z \
                                  ]
                                  enddocument


                                  enter image description here






                                  share|improve this answer



























                                    0














                                    A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



                                    documentclassarticle
                                    usepackagetikz
                                    makeatletter% https://tex.stackexchange.com/a/85531/121799
                                    longdefifnodedefined#1#2#3%
                                    @ifundefinedpgf@sh@ns@#1#3#2%

                                    makeatother
                                    newcounterCM
                                    usetikzlibrarymatrix
                                    newcommandCayleyMatrix[2][]stepcounterCM%
                                    begintikzpicture[baseline=(mat-numbervalueCM-1-1.base),inner sep=2pt,#1]
                                    matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalueCM)
                                    #2
                                    ;
                                    ifnodedefinedmat-numbervalueCM-2-1-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
                                    (mat-numbervalueCM.south west-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
                                    (mat-numbervalueCM.south west
                                    endtikzpicture
                                    begindocument
                                    [CayleyMatrix
                                    X &Y & Z \
                                    =CayleyMatrix
                                    a &b & c \
                                    a' &b' & c' \
                                    a'' & b'' & c'' \
                                    !!CayleyMatrix
                                    x &y & z \
                                    ]
                                    enddocument


                                    enter image description here






                                    share|improve this answer

























                                      0












                                      0








                                      0







                                      A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



                                      documentclassarticle
                                      usepackagetikz
                                      makeatletter% https://tex.stackexchange.com/a/85531/121799
                                      longdefifnodedefined#1#2#3%
                                      @ifundefinedpgf@sh@ns@#1#3#2%

                                      makeatother
                                      newcounterCM
                                      usetikzlibrarymatrix
                                      newcommandCayleyMatrix[2][]stepcounterCM%
                                      begintikzpicture[baseline=(mat-numbervalueCM-1-1.base),inner sep=2pt,#1]
                                      matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalueCM)
                                      #2
                                      ;
                                      ifnodedefinedmat-numbervalueCM-2-1-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
                                      (mat-numbervalueCM.south west-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
                                      (mat-numbervalueCM.south west
                                      endtikzpicture
                                      begindocument
                                      [CayleyMatrix
                                      X &Y & Z \
                                      =CayleyMatrix
                                      a &b & c \
                                      a' &b' & c' \
                                      a'' & b'' & c'' \
                                      !!CayleyMatrix
                                      x &y & z \
                                      ]
                                      enddocument


                                      enter image description here






                                      share|improve this answer













                                      A TikZ proposal. Similarly to Andrew's nice answer you can focus on typing the matrix.



                                      documentclassarticle
                                      usepackagetikz
                                      makeatletter% https://tex.stackexchange.com/a/85531/121799
                                      longdefifnodedefined#1#2#3%
                                      @ifundefinedpgf@sh@ns@#1#3#2%

                                      makeatother
                                      newcounterCM
                                      usetikzlibrarymatrix
                                      newcommandCayleyMatrix[2][]stepcounterCM%
                                      begintikzpicture[baseline=(mat-numbervalueCM-1-1.base),inner sep=2pt,#1]
                                      matrix[matrix of math nodes,ampersand replacement=&] (mat-numbervalueCM)
                                      #2
                                      ;
                                      ifnodedefinedmat-numbervalueCM-2-1-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
                                      (mat-numbervalueCM.south west-mat-numbervalueCM-1-1.south) to[out=135,in=-135]
                                      (mat-numbervalueCM.south west
                                      endtikzpicture
                                      begindocument
                                      [CayleyMatrix
                                      X &Y & Z \
                                      =CayleyMatrix
                                      a &b & c \
                                      a' &b' & c' \
                                      a'' & b'' & c'' \
                                      !!CayleyMatrix
                                      x &y & z \
                                      ]
                                      enddocument


                                      enter image description here







                                      share|improve this answer












                                      share|improve this answer



                                      share|improve this answer










                                      answered 18 mins ago









                                      marmotmarmot

                                      121k6158296




                                      121k6158296



























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