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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Matrices of rank at least k
Replies: 12   Last Post: Nov 29, 2012 1:15 PM

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Kaba

Posts: 289
Registered: 5/23/11
Re: Matrices of rank at least k
Posted: Nov 28, 2012 6:10 PM
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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

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