Minimal Gerschgorin sets. II
Bernard W. Levinger, Richard S. Varga · Pacific Journal of Mathematics · 1966
The Gerschgorin Circle Theorem, which yields n disks whose union contains all the eigenvalues of a given n X n matrix A = (fli,j), applies equally well to any matrix B = φi,i) of the set ΩA of n x n matrices with bi,i—aiti and 16^1 = 1 aitj\f 1 <; i, j ^n. This union of n disks thus bounds the entire spectrum S(ΩΛ) of the matrices in ΩA. The main result of this paper is a precise characterization of S(ΩΛ), 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.