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CholeskyDecomposition

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Returns the Cholesky decomposition, L, of a square matrix, A.

 

If A has real entries, is symmetric and is positive definite then this decomposition involves expressing it in the form  where L is a lower triangular matrix with strictly positive diagonal entries and  is its transpose. The entries of L are:

 

 

Cholesky decomposition has two main uses:

 

(a)    Suppose we draw vectors of independent normal random variables,  then  are vectors drawn from a multivariate normal distribution with covariance matrix .

(b)   A covariance matrix is non-negative definite. Perhaps the easiest way to test if a symmetric matrix is non-negative definite is to see if a Cholesky decomposition can be applied to it.

 

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