December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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8.13 LU-Factorization
INTRODUCTION
Just as positive integers and polynomials can be factored, so too a matrix can sometimes be factored into other matrices. For example, in the last section we saw that if an n × n matrix A is diagonalizable, then there exists a nonsingular matrix P and a diagonal matrix D such that P−1AP = D. When the last equation is written as A = PDP−1 we say that A has been factored or decomposed into three matrices. There are many ways of factoring an n × n matrix A, but in this section we are interested in a special type of factorization that involves triangular matrices.
The notion of a triangular matrix was introduced in Section 8.1. See page 379.
LU-Factorization
Recall, a triangular matrix is a square matrix that ...
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