Math 218: Matrices and Vector Spaces

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PA=LU Factorizations

In sage, the syntax P, L, U = A.LU(pivot='nonzero') gives the matrix equation A=PLU where P is a permutation matrix, L is lower-triangular, and U is upper-triangular. We can redefine P as its transpose P=P.T to obtain PA=LU.

In class, we require U be in row echelon form, not just upper triangular. So, we may need to do a few more reductions ourselves.