Linear Algebra and Its Applications
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.
Forstall, V., Herman, A., Li, C. K., Sze, N. S., & Yannello, V. (2011). Preservers of eigenvalue inclusion sets of matrix products. Linear algebra and its applications, 434(1), 285-293.