Date: Nov 28, 2012 6:10 PM
Author: Kaba
Subject: Re: Matrices of rank at least k
29.11.2012 1:01, quasi wrote:

>> An m x n matrix A has rank <= k

>>

>> iff some k x k submatrix of A has determinant 0,

>>

>> iff the product of the determinants of all k x k

>> submatrices of A is equal to 0.

>

> No, that's wrong -- sorry.

>

> It's something vaguely like that, but not what I said.

>

>> But the determinant of a square matrix is a polynomial in the

>> entries.

>

> I don't have time now to fix my it, but there surely is a

> polynomial P_k -- just not the one I described above.

Intuitively, I agree. Let's see if we can fill in the details.

--

http://kaba.hilvi.org