Question

I am wondering how it is possible to generate an n x n matrix in Matlab with a specific rank (number of pivot columns). I know that you can use the command randi(IMAX, m, n) to generate an m x n matrix with random entries between 1 and IMAX, but is it possible, for example, to generate a 4 x 4 matrix with random entries but only 2 pivot columns? Thanks in advance.

Answer 1

I realized that because randi(IMAX, m, n) forms an m x n matrix with as many pivot columns as possible, that it’s possible to form an n x n matrix A with k pivot columns and random entries between 1 and IMAX with the following code:

A = randi(IMAX, n, k)*randi(IMAX, k, n)

Because each of randi(IMAX, n, k) and randi(IMAX, k, n) only have k pivot columns so their product will only have k pivot columns as well.