LU factorization

(4.3 hours to learn)


The LU factorization is a factorization of a matrix into a lower triangular and an upper triangular matrix. It can be computed by recording the row operations used in Gaussian elimination. It can be a more efficient and numerically stable method of solving linear systems compared to matrix inverses.


This concept has the prerequisites:

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.
Author: Gilbert Strang
A First Course in Linear Algebra (2012)
A linear algebra textbook with proofs.
Author: Robert A. Beezer


See also

  • If the matrix is symmetric positive definite, we never need to pivot; in this case, the factorization is known as the Cholesky decomposition .