Given two matrices, $A$ ($m$ rows and $n$ columns) and $B$ ($n$ rows and $k$ columns), we want to compute matrix $A$ acting on each row of matrix $B$, and expect $mk$-dimensional matrix $C$, namely
$C = \begin{bmatrix} A B_{0} & A B_{1} & A B_{2} & \cdots & A B_{k}\end{bmatrix}$
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?