A note on polar decomposition based Geršgorin-type sets
نویسنده
چکیده
Abstract: Let B ∈ Cn×n denote a finite-dimensional square complex matrix. In [6] and [7], Professor Varga and I introduced Geršgorin-type sets which were developed from Singular Value Decompositions (SVDs) of B. In this note, our work is extended by introducing the polar SV-Geršgorin set, Γ(B). The set Γ(B) is a union of n closed discs in C, whose centers and radii are defined in terms of the entries of a polar decomposition B = Q|B|. The set of eigenvalues of B, σ(B), is contained in Γ(B). keywords: polar decomposition, Geršgorin type sets, normal matrices, eigenvalue estimates. AMS 15A18, 47A07.
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