The product field of values

Authors

Daniel Corey
Charles R. Johnson, William & MaryFollow
Ilya Spitkovsky, William & MaryFollow
Ryan Kirk
Brian Lins

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.

Recommended Citation

Corey, D., Johnson, C. R., Kirk, R., Lins, B., & Spitkovsky, I. (2013). The product field of values. Linear Algebra and its Applications, 438(5), 2155-2173.

DOI

10.1016/j.laa.2012.09.028