Vol. 17, No. 2, 1966

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Minimal Gerschgorin sets. II

Bernard Werner Levinger and Richard Steven Varga

Vol. 17 (1966), No. 2, 199–210

The Gerschgorin Circle Theorem, which yields n disks whose union contains all the eigenvalues of a given n×n matrix A = (ai,j), applies equally well to any matrix B = (bi,j) of the set ΩA of n×n matrices with bi,i = ai,i and |bi,j| = |ai,j|, 1 i, j n. This union of n disks thus bounds the entire spectrum SA) of the matrices in ΩA. The main result of this paper is a precise characterization of SA), which can be determined by extensions of the Gerschgorin Circle Theorem based only on the use of positive diagonal similarity transformations, permutation matrices, and their intersections.

Mathematical Subject Classification
Primary: 15.25
Received: 19 May 1964
Published: 1 May 1966
Bernard Werner Levinger
Richard Steven Varga