Since I’ve always been terrible at abstract linear algebra, I would request that someone do a simple problem, say finding the eigenvalues and eigenvectors of a

Since I’ve always been terrible at abstract linear algebra, I would request that someone do a simple problem, say finding the eigenvalues and eigenvectors of a 3 x 3 Hermitian matrix with three distinct eigenvalues. I’d also be curious under what circumstances the above method leads to a computational advantage.