I have a symmetric matrix, $A$, with dimension 100 x 100, of which I know the eigen vectors and eigen values ($A = U'VU$ ).
Now I want to know the eigen vectors and eigen values of $B$, which is just $A$ but with the last row and last column deleted, so it has dimension 99 x 99.
Can I accomplish this more easily than simply calculating these quantities from scratch? Can I use my eigen decomposition of $A$ to do so?
I thought I could approach this though some use of block matrix identities, but I haven't been able to come up with anything yet.