•  
  •  
 

Keywords

Matrix Polynomial, Polynomial Eigenvalue Problem, Unitary Matrix

Abstract

It is well known that the eigenvalues of any unitary matrix lie on the unit circle. The purpose of this paper is to prove that the eigenvalues of any matrix polynomial, with unitary coefficients, lie inside the annulus A_{1/2,2) := {z ∈ C | 1/2 < |z| < 2}. The foundations of this result rely on an operator version of Rouche’s theorem and the intermediate value theorem.

abs_vol30_pp577-584.pdf (29 kB)
Abstract

addendum.pdf (62 kB)
Addendum

Share

COinS
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.