# Matrix factorization

tags
Mathematics

## LU Factorization

resources
Nick Higham’s blog

An LU factorization of a $$n \times n$$ matrix $$A$$ is a factorization $$A = LU$$, where $$L$$ is lower triangular and $$U$$ is upper triangular

### LUP factorization

LU factorization with partial pivoting: $$PA = LU$$ with $$P$$ a permutation matrix.

### LDU factorization

Lower-diagonal upper factorization: $$A = LDU$$ with $$D$$ a diagonal matrix and $$L$$ and $$U$$ are uni-triangular (triangular with diagonal one).

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