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.