My math professor said once that solving the generalized eigenvalue problem
$$A\lambda = \lambda B v$$
There are two methods to use:
Method #1
Use cholesky decomposition
$$B = LL^T$$
Solve $Y$
$$AY = L$$
Take the inverse of $L^T$ and multiply it with $Y$
$$X = Y*(L^T)^{-1}$$
Then you solve the eigendecomposition
$$X\lambda = \lambda v$$
And now you found the eigenvalues $\lambda$ and the eigenvectors $v$
Method #2
Take the inverse of $B$ and solve the eigendecomposition
$$B^{-1}A\lambda = \lambda v$$
And now you found the eigenvalues $\lambda$ and the eigenvectors $v$
Question:
According to my math professor, method #1 is much more prefered than method #2.
My question is: why?