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Strict double diagonal dominance in Euclidean Jordan algebras

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
436
Issue
7
Identifiers
DOI: 10.1016/j.laa.2011.11.012
Keywords
  • Euclidean Jordan Algebras
  • Directed Graphs
  • Brauer Ovals
  • Strict Double Diagonal Dominance
  • Generalized Strict Diagonal Dominance
  • H-Property
  • Schur Complements
Disciplines
  • Mathematics

Abstract

Abstract In the first part of the paper, we deal with Euclidean Jordan algebraic generalizations of some results of Brualdi on inclusion regions for the eigenvalues of complex matrices using directed graphs. As a consequence, the theorems of Brauer–Ostrowski and Brauer on the location of eigenvalues are extended to the setting of Euclidean Jordan algebras. In the second part, motivated by the work of Li and Tsatsomeros on the class of doubly diagonally dominant matrices with complex entries and its subclasses, we present some inter-relations between the H-property, generalized strict diagonal dominance, invertibility, and strict double diagonal dominance in Euclidean Jordan algebras. In addition, we show that in a Euclidean Jordan algebra, the Schur complements of a strictly doubly diagonally dominant element inherit this property.

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