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

It's not really so clear what you are aiming for.

But in order to create a matrix B with specific rank k, from a matrix A (with rank at least k), you may like to utilize svd and proceed like:

>>> A= rand(7, 5);
>>> rank(A)
ans =  5
>>> [U, S, V]= svd(A);
>>> k= 3;
>>> B= U(:, 1: k)* S(1: k, 1: k)* V(:, 1: k)';
>>> rank(B)
ans =  3