A New Estimation for Eigenvalues of Matrix Power Functions

Abstract

We give an estimation for the eigenvalues of matrix power functions. In particular, it has been shown that $$\lambda({(A+B)^p})\leq\lambda({2^{p-1}}({A^p}+{B^p}-\gamma I))\;(P \geq2)$$ for all positive semi-definite matrices A, B, where γ is a positive constant. This provides a sharper bound for the known estimation for eigenvalues.