A Note on the Eigenvalues of Hermitian Matrices
David Slepian, Henry J. Landau · SIAM Journal on Mathematical Analysis · 1978
Two simple relations are derived that connect the eigenvalues of a Hermitian matrix with those of the submatrix obtained by deleting a row and the corresponding column. The relations, which readily establish the interlacing of these two sets of eigenvalues, are used to obtain an upper bound for the largest eigenvalue and a lower bound for the smallest eigenvalue of a Hermitian matrix.