2
$\begingroup$

I have a general $m\times m$ matrix whose antisymmetric part is non singular. What is the minimum rank of that matrix?

Improve this question
$\endgroup$
1
  • 4
    $\begingroup$ I hope you won't find it rude if I ask where this problem came from? It perfectly well could be a lemma that came up somewhere, but it would also make a good exercise in an advanced linear algebra course. In the mean time, here is a hint: The anti-symmetrization of $A$ is $A - A^T$. What do you know about $\mathrm{rank}(A+B)$? $\endgroup$
    – David E Speyer
    Commented Feb 15, 2012 at 11:01

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .