(3.4 hours to learn)
Gaussian elimination is an algorithm for solving systems of linear equations, computing matrix inverses, and computing the LU factorization of a matrix.
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)
→ 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
→ 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"
- 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 .
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