Some Bounds for the Spectral Radius (SR)

Abstract

The spectral radius  of a square matrix ( ) is the largest absolute value of any eigenvalue of  . I divided this research into two parts, the first part in which I mention the definition of the spectral radius and the spectral norm, then I mention some of the characteristics related to the spectral radius and the spectral norm that I need in my research, along with proof of some of them.

In the second part of the research, I discuss a group of inequalities and provide proof of them. I will rely on some well-known inequalities and some well-known characteristics about spectral radius and spectral norm.

Keywords: Nonnegative matrix (~M), Positive matrix (+M), Spectral radius (SR), Pinching inequalities