Document Type

Article

Department/Program

Mathematics

Journal Title

Linear Algebra and Its Applications

Pub Date

2013

Volume

438

Issue

5

First Page

2155

Abstract

For two n-by-n matrices, A, B, the product field of values is the set P(A, B) = {< AX, X > < Bx, X > : X is an element of C-n, parallel to X parallel to = 1}. In this paper, we establish basic properties of the product field of values. The main results are a proof that the product field is a simply connected subset of the complex plane and a characterization of matrix pairs for which the product field has nonempty interior. (C) 2012 Elsevier Inc. All rights reserved.

DOI

10.1016/j.laa.2012.09.028

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