Let $A$ be a square matrix that commutes with its transpose. Show that the nullspaces of $A$ and $A^T$ coincide.

Question

Am completely stuck on this, any help would be appreciated.

I appreciate that this isn't the right way to go about things, but I am completely flummoxed. Don't even know how to start this question :( — thesmallprint, Apr 21 '17 at 18:49

score 2 · Accepted Answer · answered Apr 21 '17 at 18:50

2

Hint: Suppose $Ax = 0$ and look at $\|A^Tx\|^2 = x^T A A^T x$

answered Apr 21 '17 at 18:50

Michael Biro

1 Answers1