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NCAlgebra :: NCMatrix * NCMatrix

NCMatrix * NCMatrix -- Product of NCMatrices

Synopsis

Description

This command allows for the product of composable NCMatrices (or ordinary matrices over the base).

i1 : B = threeDimSklyanin(QQ,{1,1,-1},{x,y,z})
--Calling Bergman for NCGB calculation.
--running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12438-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12438-0/3.ter ... Complete!

o1 = B

o1 : NCQuotientRing
i2 : M = ncMatrix {{x, y, z}}

o2 = | x  y  z |

o2 : NCMatrix
i3 : sigma = ncMap(B,B,{y,z,x})

o3 = NCRingMap B <--- B

o3 : NCRingMap
i4 : N = ncMatrix {{M},{sigma M}, {sigma sigma M}}

o4 = | x  y  z |
     |         |
     | y  z  x |
     |         |
     | z  x  y |

o4 : NCMatrix
i5 : N' = ncMatrix {{sigma sigma M}, {sigma M}, {M}}

o5 = | z  x  y |
     |         |
     | y  z  x |
     |         |
     | x  y  z |

o5 : NCMatrix
i6 : N*N'

     |     2        2            |
o6 = |   2y       2x     2yx+2xy |
     |                           |
     |     2                 2   |
     |   2x     2yx+2xy    2y    |
     |                           |
     |              2        2   |
     | 2yx+2xy    2y       2x    |

o6 : NCMatrix
i7 : N'*N

     |      2                   2    2        2 |
o7 = |  yz+y -xz+xy  -yz+yx+xz+x    y +yx+xy+x  |
     |                                          |
     |            2    2        2       2       |
     | -yz+yx+xz+x    y +yx+xy+x    yz+y -xz+xy |
     |                                          |
     |   2        2       2                   2 |
     |  y +yx+xy+x    yz+y -xz+xy  -yz+yx+xz+x  |

o7 : NCMatrix