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

A matrix of rank 1 can be created by the outer product of two vectors, for example:

A = randn(10,1) * randn(1,10);

Add together k of these and you will have a matrix of rank k. Like this:

>> A = zeros(10);
>> for i = 1:4, A = A + randn(10,1) * randn(1,10); end
>> rank(A)

ans =  4