A note on polar decomposition based Geršgorin-type sets |
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Authors: | Laura Smithies |
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Institution: | Kent State University, Department of Mathematical Sciences, Kent, OH 44242, United States |
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Abstract: | Let B∈Cn×n denote a finite-dimensional square complex matrix. In L. Smithies, R.S. Varga, Singular value decomposition Geršgorin sets, J. Linear Algebra Appl. 417 (2004) 370-380; N. Fontes, J. Kover, L. Smithies, R.S. Varga, Singular value decomposition normally estimated Geršgorin sets, Electron. Trans. Numer. Anal. 26 (2007) 320-329], 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, ΓPSV(B). The set ΓPSV(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 ΓPSV(B). |
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Keywords: | 15A18 47A07 |
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