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curriculum/challenges/chinese/10-coding-interview-prep/rosetta-code/lu-decomposition.md
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# --description--
Every square matrix $A$ can be decomposed into a product of a lower triangular matrix $L$ and a upper triangular matrix $U$, as described in [LU decomposition](<https://en.wikipedia.org/wiki/LU decomposition>).
Every square matrix $A$ can be decomposed into a product of a lower triangular matrix $L$ and a upper triangular matrix $U$, as described in [LU decomposition](https://en.wikipedia.org/wiki/LU decomposition).
$A = LU$
It is a modified form of Gaussian elimination.
While the [Cholesky decomposition](<http://rosettacode.org/wiki/Cholesky decomposition>) only works for symmetric, positive definite matrices, the more general LU decomposition works for any square matrix.
While the [Cholesky decomposition](http://rosettacode.org/wiki/Cholesky decomposition) only works for symmetric, positive definite matrices, the more general LU decomposition works for any square matrix.
There are several algorithms for calculating $L$ and $U$.