How would you transpose a binary matrix?

Question

I have binary matrices in C++ that I repesent with a vector of 8-bit values.

For example, the following matrix:

1 0 1 0 1 0 1
0 1 1 0 0 1 1
0 0 0 1 1         


        

Answer 1

My suggestion is that, you don't do the transposition, rather you add one bit information to your matrix data, indicating whether the matrix is transposed or not.

Now, if you want to multiply a transposd matrix with a vector, it will be the same as multiplying the matrix on the left by the vector (and then transpose). This is easy: just some xor operations of your 8-bit numbers.

This however makes some other operations complicated (e.g. adding two matrices). But in the comment you say that multiplication is exactly what you want to optimize.