- #1
D.K.
- 12
- 0
Homework Statement
Prove that for any m x s matrix A and any s x n matrix B it holds that:
rank(A) + rank(B) - s
is less or equal to:
rank(AB)
The Attempt at a Solution
Obviously, the following are true:
- rank(A) is less or equal to s,
- rank(B) is less or equal to s,
- rank(AB) is less or equal to both rank(A) and rank(B).
So it is possible to prove:
rank(A) + rank(B) - 2s is less or equal to rank(AB).
Really don't know what can be done next. Thanks for any help on this.