# 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

## 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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