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NCAlgebra :: Matrix * NCMatrix

Matrix * 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/M2-12488-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12488-0/3.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 : L = map(QQ^3,QQ^3,{{2,0,0},{1,2,0},{1,2,3}})

o5 = | 2 0 0 |
     | 1 2 0 |
     | 1 2 3 |

              3        3
o5 : Matrix QQ  <--- QQ
i6 : L*N

o6 = |    2x       2y       2z   |
     |                           |
     |   2y+x     2z+y     z+2x  |
     |                           |
     | 3z+2y+x  2z+y+3x  z+3y+2x |

o6 : NCMatrix