Strict double diagonal dominance in Euclidean Jordan algebras

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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.

AMS classification

17C55
15A18
05C20

Keywords

Euclidean Jordan algebras
Directed graphs
Brauer ovals
Strict double diagonal dominance
Generalized strict diagonal dominance
H-property
Schur complements

Cited by (0)

The author is grateful to Professor M.S. Gowda for helpful suggestions.