A note on improvement on bounds for nonmaximal eigenvalues of symmetric positive matrices

In this work, we improve the lower and upper bounds obtained by Zhang and Luo [X. Zhang, R. Luo, Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices, Czechoslovak Math. J. 52 (127) (2002) 537–544] for the nonmaximal eigenvalue λn−1(A) of a symmetric positive matrix.