Given two matrices, A_m*n (m rows and n columns), and B_n*k (n rows and k columns), now we want to compute matrix A acting on each row of matrix B, and expect (m*k)-dimensional matrix C, namely
C=A * (B_{0}) | ( A * (B_{1}) ) | ( A * (B_{1}) ) |...| ( A * (B_{k}) )
For example, let
A=matrix{{a_00, a_01, a_02},
{a_10, a_11, a_12}},
B=matrix{{b_00, b_01, b_02, b_03},
{b_10, b_11, b_12, b_13},
{b_20, b_21, b_22, b_23}}
namely, m=2, n=3, k=4
C=matrix{{a_00*b_00+a_01*b_10+a_02*b_20, a_00*b_01+a_01*b_11+a_02*b_21, a_00*b_02+a_01*b_12+a_02*b_22, a_00*b_03+a_01*b_13+a_02*b_23},
{a_10*b_00+a_11*b_10+a_12*b_20, a_10*b_01+a_11*b_11+a_12*b_21, a_10*b_02+a_11*b_12+a_12*b_22, a_10*b_03+a_11*b_13+a_12*b_23} }
I could do a loop over k, and then concatenate column by column. But this is not efficient enough, when k is very large, say 10,000.
Any tips?
