Algebraic relation between symmetric matrix and its principal submatrix?

Question

Let $A$ be a $n\times n$ real symmetric matrix and $B$ be $m\times m$ real symmetric matrix where $n>m$. $B$ be a principal submatrix of $A$ (i.e) (obtained by deleting both $i$-th row and $i$-th column for some values of $i$). Then can we establish some relationship between the characteristic polynomial or eigenvalues of $A$ and $B$?