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.

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