Numerical ranges as circular discs.
Journal
Appl. Math. Lett.
Journal Volume
24
Journal Issue
12
Pages
2115-2117
Date Issued
2011
Author(s)
Abstract
We prove that if a finite matrix A of the form [aIB0C]is such that its numerical range W(A) is a circular disc centered at a, then a must be an eigenvalue of C. As consequences, we obtain, for any finite matrix A, that (a) if ∂W(A) contains a circular arc, then the center of this circle is an eigenvalue of A with its geometric multiplicity strictly less than its algebraic multiplicity, and (b) if A is similar to a normal matrix, then ∂W(A) contains no circular arc. © 2011 Elsevier Ltd. All rights reserved.
Type
journal article