Suppose I have a LxM matrix A and a MxN matrix B. I can multiply them a I have learned by taking the rows of A and the columns of B and take the inner product of them.
But I can also do it in another way. I see in A columns and in B rows. Then I take the Kronecker product of the first column of A and the first row of B, which gives a matrix. I do the same for the second column of A and the second row of B and add this resulting matrix to the first one. Do this for all columns of A and rows of B and add the resulting matrices. You will get the matrix product of A and B.
Example:
A=(1 2) B=(4 3)
(3 4) (2 1)
(1)*(4 3)=(4 3) (2)*(2 1)=(4 2)
(3) (12 9) (4) (8 4)
Add:
(8 5)
(20 13)
I there some decomposition involved?