# Cholesky decomposition

In

mathematics, the

**Cholesky decomposition** of

matrix theory is a special case of the

LU decomposition which can only be done if

*A* is a

symmetric positive definite matrix with

real entries.

You can decompose *A* into:

*A* = *L* *L*^{T}

where

*L* is a lower triangular matrix with positive diagonal entries, and

*L*^{T} denotes the transpose of

*L*.

For a brief history of the theorem and an explanation of its name see the entry on the Cholesky algorithm, decomposition, factorisation, etc. in
For an obituary of Andre-Louis Cholesky see

For a nice account in French by Yves Dumont see