How to create a rank k matrix using MATLAB?

Question

Im looking to create a matrix of rank k. The dimension of the matrix is m x n. The input k satisfies that condition that k < min(

Answer 1

Well, a trivial method is to produce a matrix that looks like:

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

i.e. k columns of the identity matrix, then repeat the last column n-k times (or m-k times, depending on orientation).