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Preservers of eigenvalue inclusion sets of matrix products
Sze, Nung-Sing Forstall, Virginia Herman, Aaron Li, Chi-Kwong Yannello, Vincent
Sze, Nung-Sing
Forstall, Virginia
Herman, Aaron
Li, Chi-Kwong
Yannello, Vincent
Abstract
For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the union of Cassini ovals, and the Ostrowski's set. Characterization is obtained for maps Phi on n x n matrices satisfying S(Phi(A)Phi(B)) = S(AB) for all matrices A and B. (C) 2010 Elsevier Inc. All rights reserved.
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2011-01-01
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Mathematics
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10.1016/j.laa.2010.08.016