row-echelon matrix form (not reduced)

what is row-echelon matrix form (not reduced) in matlab?

Answer 1

[Nagabhushan SN]

lu(A)

performs LU factorization of a matrix. So, you can get upper triangular matrix from there. Not sure though if it performs Gauss reduction

[L,U,P] = lu(A);

[Brahim]

what does the P stand for?

[Joe]

Permutation

Answer 2

[Ivan van der Kroon]

With rref you will produce the reduced row echelon form, see

doc rref

But a non-reduced form is not unique. See for instance wikipedia: http://en.wikipedia.org/wiki/Gaussian_elimination. You can multiply individual rows with a scalar and/or add rows to other rows. It is in echelon form as long as it is upper-triangular.

[Eric T]

That's fine, though: eigenvectors are not unique either, and there is a function that returns eigenvectors. It wouldn't be that hard to produce it, as you said, as long as it is in upper triangular form (this is like LU factorization which is also underdetermined, but matlab does). I think it would be instructive for Matlab to provide this for my students....I could have them compare rref(A) and (the nonexistent) ref(A)...

[Carol Hurwitz]

yes ,it would be a good idea, especially since Lay's Linear Algebra seems to prefer Matlab

[Charles Daniels]

it should be implemented the same way TI does in their calculators, for consistency