15.3.5 LU decomposition
The LU decomposition of a square matrix A is P A=L U, where P is a
permutation matrix, L is lower triangular with ones on the diagonal,
and U is upper triangular.
The lu command finds the LU decomposition of a matrix.
-
lu takes
A, a square matrix.
- lu(A) returns a list [p,L,U] where p is a
permutation that determines P, and P, L and U are the LU
decomposition of A.
The permutation matrix P is defined from p by:
| Pi,p(i)=1, Pi,j=0 if j ≠ p(i).
|
In other words, it is the identity matrix where the rows are permuted
according to the permutation p. You can get the permutation matrix
from p by P:=permu2mat(p) (see Section 12.2.6).
Example
| A:=[[3.,5.],[4.,5.]]:;
(p,L,U):=lu(A) |
Verification:
Note that the permutation is different for exact input (the choice of
pivot is the simplest instead of the largest in absolute value).