I am trying to find an analytical method to find the number of valid elements in a matrix*matrix^T from the matrix without the need of doing the multiplication. I call valid elements all elements which multiplication is not zero. I'll give a brief example:
Say we have this matrix A:
1 2 0
4 0 0
2 3 5
and its transposed T:
1 4 2
2 0 3
0 0 5
Let's call Zij = Number of elements valid of row i of A when multiply by column j of T. For instance,
Z00 = N_valids(1*1+2*2+0*0) = 2
Z10 = N_valids(4*1+0*2+0*0) = 1
Following this we'll have Z:
2 1 2
1 1 1
2 1 3
I would like to know if somebody knows how to find out Z from A. The diagonal elements its clear, but not the rest...