Learn Cholesky Algorithm for Reducing Matrices by Thursday

[stunner5000pt]

This is not a homework question per se, but i would like to understnad the cholesky method of reducing matrices before my test on thursday

up till now every search on the net has found me computer algorithms but i can't really understand those and apply those pracitcally

so givne some matrix
$$\left(\begin{array}{ccc} 2&-1&0\\-1&2&-1\\0&-1&2\end{array}\right)$$
i know for the first column let $l_{11} = \sqrt{a_{11}}$
and thereafter $$l_{j1}=\frac{a_{j1}}{l_{11}}$$
but what happens for l21,l22, and so on??
Please help me out i really need to understand this!

Thank you in advance

 

[Mark44]

Presumably the OP found an answer to the question, but if not or if others have the same question, here's some more information, based on this wiki article: https://en.wikipedia.org/wiki/Cholesky_decomposition
Starting with a Hermitian positive-definite matrix A, Cholesky decomposition decomposes A into a matrix product LL*, with L being a lower triangular matrix with real and positive entries on the diagonal, and L*, the complex conjugate transpose of L.
A few examples are shown on the wiki page in the link above.