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Linear operators preserving the sign-real spectral radius

✍ Scribed by Bojana Zalar

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 105 KB
Volume: 301
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00183-4

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✦ Synopsis

Define the sign-real spectral radius of a real n × n matrix A as ρ s 0 (A) = max S∈S ρ 0 (SA), where ρ 0 (A) = max{|λ|; λ a real eigenvalue of A} is the real spectral radius of A and S denotes the set of signature matrices, i.e. S = {S; |S| = I}, the absolute value of matrices being meant entrywise. In this paper we show that linear invertible operators F on the space of n × n real matrices M n (R) preserving the sign-real spectral radius are exactly the operators of the form F (A) = P T D -1 SA (T) DP with P a permutation matrix, D a diagonal matrix and S a signature matrix.

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