I am trying to generate 500 matrices whose null spaces are non-zero, integer vectors.
I currently generate the matrices by using
rand() to choose a number between 1 and 5. I find the kernel by passing the matrix to EigenLib's
kernel() function. However, my matrix generation algorithm is entirely insufficient because (generally) 19/20 of the kernels are the zero vector.
How do I generate matrices whose null spaces will have integer, non-zero vectors?