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Generalizations of the Ostrowski–Brauer theorem

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
364
Identifiers
DOI: 10.1016/s0024-3795(02)00537-2
Disciplines
  • Mathematics

Abstract

Abstract The main theorem of this paper, which generalizes the Ostrowski–Brauer theorem and its previous extensions, provides conditions necessary and sufficient for the singularity of an irreducible matrix A=(a ij)∈ C n×n satisfying the conditions |a ii||a jj|⩾R i(A)R j(A), where R k(A)=∑ j≠k|a kj|, k=1,…,n, for all i≠ j such that | a ij |+| a ji |≠0 and implies a new description of the location of matrix eigenvalues in terms of ovals of Cassini and Gerschgorin circles.

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