Singular value decomposition Geršgorin sets

In this note, we introduce the singular value decomposition Geršgorin set, ΓSV (A), of an N × N complex matrix A, where N ∞. For N finite, the set ΓSV (A) is similar to the standard Geršgorin set, Γ (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, ΓSV (A) is constructed using column sums of singular value decomposition matrix coefficients, whereas Γ(A) is constructed using row sums of the matrix values of A. In the case N = ∞, the set ΓSV(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.