Sorry, I realized that, I stated the problem very incomplete. Let "f" be such a quadratic function x'Ax which is also a positive definite function. We know that is eigenvalues of "A" are positive in this situation. "A" is such a matrix that its diagonal depends on a variable, let say "y" to this variable. I wonder is "f" increasing of "y". Does eigenvalues or eigenvectors show something about? Thanks a lot.