Cholesky Decomposition¶
Useful if we want to decomposie a positive-definite Hermetian matrix into 2 parts. First is a lower triangular matrix and the second is its conjugate transpose.
\(A = L L^T\)
Calculating the inverse¶
We can use this decomposition to calculate the inverse:
\(A^{-1} = (L^{-1})^T (L^{-1})\)
It is easier to calculate the inverse of a triangular matrix and in general it provides more stable solutions that direct inverting.
More here: http://www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdf