# MultidimensionalMatrix * MultidimensionalMatrix -- product of multidimensional matrices

## Synopsis

• Operator: *
• Usage:
M * N
• Inputs:
• M, , a multidimensional matrix of shape $k_1\times\cdots\times k_r$
• N, , a multidimensional matrix of shape $l_1\times\cdots\times l_s$ with $k_r = l_1$
• Outputs:
• , the convolution (or product) $M * N$, which is a multidimensional matrix of shape $k_1\times\cdots\times k_{r-1}\times l_2\times\cdots\times l_s$

## Description

 i1 : M = randomMultidimensionalMatrix {4,3} o1 = {{8, 1, 3}, {7, 8, 3}, {3, 7, 8}, {8, 5, 7}} o1 : 2-dimensional matrix of shape 4 x 3 over ZZ i2 : N = randomMultidimensionalMatrix {3,2} o2 = {{8, 5}, {2, 3}, {6, 3}} o2 : 2-dimensional matrix of shape 3 x 2 over ZZ i3 : M * N o3 = {{84, 52}, {90, 68}, {86, 60}, {116, 76}} o3 : 2-dimensional matrix of shape 4 x 2 over ZZ i4 : N' = randomMultidimensionalMatrix {3,2,4} o4 = {{{6, 8, 6, 9}, {3, 7, 6, 9}}, {{6, 2, 6, 0}, {2, 6, 9, 3}}, {{5, 6, 3, ------------------------------------------------------------------------ 5}, {7, 7, 9, 4}}} o4 : 3-dimensional matrix of shape 3 x 2 x 4 over ZZ i5 : M * N' o5 = {{{69, 84, 63, 87}, {47, 83, 84, 87}}, {{105, 90, 99, 78}, {58, 118, ------------------------------------------------------------------------ 141, 99}}, {{100, 86, 84, 67}, {79, 119, 153, 80}}, {{113, 116, 99, ------------------------------------------------------------------------ 107}, {83, 135, 156, 115}}} o5 : 3-dimensional matrix of shape 4 x 2 x 4 over ZZ