0
$\begingroup$

If A is matrix m by n and B is matrix n by r

The rank of matrix AB ought to be minimum of rank(A) or rank(B) how may i prove this? Thanks

  • 0
    Pretty sure the conclusion is false. Why do you think it's true?2012-09-07
  • 1
    Hint: two nonzero matrices with a product that is zero will suffice as a counterexample2012-09-07
  • 0
    rank($AB$) $\leq$ min(rank($A$),rank($B$)). Equality is not guaranteed.2012-09-07
  • 0
    On the other side, $\text{rank}(AB) \ge \text{rank}(A) + \text{rank}(B) - n$.2012-09-07

1 Answers 1