Introduction to Computational Linear Algebra

Chapter 3

Gauss Elimination and LU

Decompositions of Matrices

In this chapter, our main objective is to prove the general decomposition

of any matrix into the product of a unit lower triangular matrix by

an upper triangular one. Such decompositions formalize the procedures

for solving systems of linear equations by Gauss elimination. This material is

at the heart of matrix computations and constitutes the basis for computing

determinant and inverse of square matrices. More specific details can be found

in books such as Ciarlet [19], Poole [56], Trefethen [69], and Golub and Van

Loan [33].

Gauss reduction is the main procedure for obtaining an LU decomp ...