Advanced Engineering Mathematics, 7th Edition

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 ...