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5.1.77 ludecomp
Syntax:
ludecomp ( matrix_expression )
Type:
- list
Purpose:
- Computes the LU-decomposition of an (m x n) matrix.
The matrix, A say, must consist of numbers, only. This means that
when the basering represents some
then all entries of A must come from the ground field K.
The LU-decomposition of A is a triple of matrices P, L, and U such that
- P * A = L * U,
- P is an (m x m) permutation matrix, i.e., its rows/columns form the
standard basis of K^m,
- L is an (m x m) matrix in lower triangular form with all diagonal
entries equal to 1, and
- U is an (m x n) matrix in upper row echelon form.
From these conditions, it easily follows that also A = P * L * U holds,
since P is self-inverse.
list L=ludecomp(A); fills a list L with the three above entries
P, L, and U.
Example:
See
luinverse.
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