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Hi,

is there any numerical invariant that would characterize the rank of a non-square matrix, similar to the determinant for square matrices? I.e. having a matrix nxm, with n<m, I'm looking for a number that would be zero if the rank of the matrix is smaller than n and nonzero if the rank is n. By "similar to the determinant" I mean that it would be some number, which you could obtain by doing some arithmetic operations on the entries, but without the necessity to perform Gaussian Elimination.

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# Determinant of a non-square matrix?

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