Linear Algebra for Computer Science

Question

Let 2 square matrices M and N each have rank 1. What can you say about the rank of MN?

Answer 1

Generally speaking, rank(M*N) <= min(rank(M), rank(N)).

So in this case, rank(M*N)<=1.

It's possible that rank(M*N=0.

Ex:

If

M = [[0, 1], [0,1]]

N = [[1, 0], [1,0]]

Then

M*N = [0, 0], [0, 0]]

and

rank(M) = rank(N) = 1

rank(M*N) = 0