# Gaussian elimination

(3.4 hours to learn)

## Summary

Gaussian elimination is an algorithm for solving systems of linear equations, computing matrix inverses, and computing the LU factorization of a matrix.

## Context

This concept has the prerequisites:

- linear systems as matrices (Gaussian elimination is a method for solving linear systems.)

## Core resources (read/watch one of the following)

## -Free-

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

Location:
Lecture "Elimination with matrices"

→ A First Course in Linear Algebra (2012)

A linear algebra textbook with proofs.

→ Khan Academy: Linear Algebra

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Sections 2.2, "The idea of elimination," and 2.3, "Elimination using matrices," pages 45-61

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 4.1, "Gaussian elimination and the theory of linear systems"

## See also

- Gaussian elimination can be viewed as factorizing a matrix into a lower triangular and an upper triangular matrix.
- If the matrix is symmetric positive definite, we never need to pivot; in this case, the algorithm is known as the Cholesky decomposition .