- #1
GargleBlast42
- 28
- 0
"Determinant" of a non-square matrix?
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.
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.