Wishart Distribution - Bartlett Decomposition

The Bartlett decomposition of a matrix from a p-variate Wishart distribution with scale matrix V and n degrees of freedom is the factorization:

where L is the Cholesky decomposition of V, and:

\mathbf A = \begin{pmatrix} \sqrt{c_1} & 0 & 0 & \cdots & 0\\ n_{21} & \sqrt{c_2} &0 & \cdots& 0 \\ n_{31} & n_{32} & \sqrt{c_3} & \cdots & 0\\ \vdots & \vdots & \vdots &\ddots & \vdots \\ n_{p1} & n_{p2} & n_{p3} &\cdots & \sqrt{c_p} \end{pmatrix}

where and independently. This provides a useful method for obtaining random samples from a Wishart distribution.

Read more about this topic:  Wishart Distribution