I'm not really a math person, and apologize if the question here is too simple. I've ended up with the following type of question for a few Lie groups, but state it for SO(n). I start with a subgroup ...
Suppose a square, dense, symmetric matrix $A$ has been factorized into $L$ and $U$ components by performing a LU decomposition. Now let $B = A+\lambda I$. Is there any way to efficiently compute the ...
Which would be the most efficient way (in computational time) to compute tr(inv(H)), where H is a (dense) square matrix? In my particular problem I also have a LU decomposition of H already ...