Category:Definitions/LU Factorizations

This category contains definitions related to LU Factorizations.
Related results can be found in Category:LU Factorizations.

Let $\mathbf A$ be a square matrix.

An LU factorization of $\mathbf A$ is a factorization of $\mathbf A$ in the form:

$\mathbf A = \mathbf {L U}$

where:

$\mathbf L$ is a lower triangular matrix and $\mathbf U$ is a upper triangular matrix.

It is usual to arrange this so that either $\mathbf L$ or $\mathbf U$ has a unit diagonal.