矩阵分解（decomposition,factorization）是多半将矩阵拆解为数个三角形矩阵（triangular matrix），依使用目的的不同，可分为几类。

在数值分析，矩阵分解常常用来实现一些矩阵运算的快速算法。

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.