Singular value decomposition Geršgorin sets

✍ Scribed by Laura smithies; Richard S. Varga

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 179 KB
• Volume: 417
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2005.10.032

✦ Synopsis

In this note, we introduce the singular value decomposition Geršgorin set, SV (A), of an N × N complex matrix A, where N ∞. For N finite, the set SV (A) is similar to the standard Geršgorin set, (A), in that it is a union of N closed disks in the complex plane and it contains the spectrum, σ (A), of A. However, SV (A) is constructed using column sums of singular value decomposition matrix coefficients, whereas (A) is constructed using row sums of the matrix values of A. In the case N = ∞, the set SV (A) is defined in terms of the entries of the singular value decomposition of a compact operator A on a separable Hilbert space. Examples are given and applications are indicated.