# Cholesky decomposition

## Matrix decomposition method / From Wikipedia, the free encyclopedia

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In linear algebra, the **Cholesky decomposition** or **Cholesky factorization** (pronounced /ʃəˈlɛski/ *shə-LES-kee*) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924.[1]
When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.[2]