Preservers of Eigenvalue Inclusion Sets
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 Î¦ on n Ã— n matrices satisfying S (Î¦ (A) - Î¦ (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 (Î¦ (A)) for every matrix A. © 2010 Elsevier Inc. All rights reserved.
Brauer region, Cassini ovals, Eigenvalue inclusion sets, Gershgorin region, Ostrowski region, Preservers
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