Preservers of Eigenvalue Inclusion Sets

Authors

James Hartman, The College of Wooster
A. Herman, College of William and Mary
C. Li, College of William and Mary

Publication Date

2010

Document Type

Article

Issue

5

Abstract

For a square matrix A, let S (A) be an eigenvalue inclusion set such as the Gershgorin region, the Brauer region in terms of Cassini ovals, and the Ostrowski region. Characterization is obtained for maps Φ on n × n matrices satisfying S (Φ (A) - Φ (B)) = S (A - B) for all matrices A and B. From these results, one can deduce the structure of additive or (real) linear maps satisfying S (A) = S (Φ (A)) for every matrix A. © 2010 Elsevier Inc. All rights reserved.

Keywords

Brauer region, Cassini ovals, Eigenvalue inclusion sets, Gershgorin region, Ostrowski region, Preservers

Recommended Citation

Hartman, James; Herman, A.; and Li, C., "Preservers of Eigenvalue Inclusion Sets" (2010). Linear Algebra and its Applications, (5), 1038-1051. 10.1016/j.laa.2010.04.028. Retrieved from https://openworks.wooster.edu/facpub/149