I implemented three methods for inversion of a matrix, all are classic. I wanted to test for the most generalized method, while taking efficiency into account.
For Cholesky decomposition, which is relatively efficient, the matrix $A$ should be positive or semi positive definite. It is known for a matrix $A$ to be positive definite, its eigenvalues must be positive. Now, in the case of rotation matrices, their eigenvalues represent modes "think of frequency, if that is a proper interpretation", and therefore are complex "or real". In such case...is there a such thing as a reliable Cholesky decomposition for the inversion of an arbitrary rotation matrix.
Note: $R^{-1}=R^T$ for rotation matrices "orthogonal", but still, i would like to test for explicit inversion using Cholesky method with forward and backward substitution