Figure Properties - SERC

P Row permutation matrix satisfying the equation L*U = P*X, or
L*U = P*X*Q. Used for numerical stability.
Q Column permutation matrix satisfying the equation P*X*Q = L*U.
Used to reduce fill-in in the sparse case.
Examples Example 1. Start with
A = [ 1 2 3
4 5 6
7 8 0 ];
To see the LU factorization, call lu with two output arguments.
[L1,U] = lu(A)
L1 =
0.1429 1.0000 0
0.5714 0.5000 1.0000
1.0000 0 0
U =
7.0000 8.0000 0
0 0.8571 3.0000
0 0 4.5000
Notice that L1 is a permutation of a lower triangular matrix: if you switch rows
2 and 3, and then switch rows 1 and 2, the resulting matrix is lower triangular
and has 1s on the diagonal. Notice also that U is upper triangular. To check that
the factorization does its job, compute the product
L1*U
which returns the original A. The inverse of the example matrix, X = inv(A),
is actually computed from the inverses of the triangular factors
X = inv(U)*inv(L1)
Using three arguments on the left side to get the permutation matrix as well
[L2,U,P] = lu(A)
lu
2-1389