Last time we took a first look at the Cholesky decomposition, being the unique way to represent a positive definite symmetric square matrix , formed by switching the row and column indices of each element so that

Finally we noted that, like the Jacobi decomposition, the Cholesky decomposition is useful for solving simultaneous equations, inverting matrices and so on, but left the implementation details to this post.

**M**as the product of a lower triangular matrix**L**having strictly positive elements on its leading diagonal, and by definition zeroes everywhere above it, with its upper triangular transpose**L**

^{T}

**L**

^{T}

_{ij}=

**L**

_{ji}

**M**=

**L**×

**L**

^{T}

Finally we noted that, like the Jacobi decomposition, the Cholesky decomposition is useful for solving simultaneous equations, inverting matrices and so on, but left the implementation details to this post.

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