LU Decomposition

In Mathematica, the function LUDecomposition factors a matrix

m

into the form P L U, where P is a permutation matrix, L is a lower triangular matrix, and U is an upper triangular matrix. The decomposition fails for most matrices

m

with zero-valued minors, such as

0	1	1
0	0	0
0	1	0

, although P L U may be close to

m

.