Strict diagonal dominance and a Geršgorin type theorem in Euclidean Jordan algebras

DOI10.1016/j.laa.2009.02.016zbMath1168.15016OpenAlexW2171888315MaRDI QIDQ1019643

M. Seetharama Gowda, Melania M. Moldovan

Publication date: 4 June 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.02.016

zbMATH Keywords

Euclidean Jordan algebrasHermitian matriceseigenvaluesmatrix algebrasquaternionsdiagonal dominanceoctonionsPeirce decompositionLevy-Desplanques theoremGeršgorin theoremJordan spin algebraJordan frame

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Algebraic systems of matrices (15A30) Idempotents, Peirce decompositions (17C27)

Related Items (9)

Schur complements, Schur determinantal and Haynsworth inertia formulas in Euclidean Jordan algebras ⋮ Some majorization inequalities in Euclidean Jordan algebras ⋮ Strict double diagonal dominance in Euclidean Jordan algebras ⋮ More results on Schur complements in Euclidean Jordan algebras ⋮ Some inequalities involving determinants, eigenvalues, and Schur complements in Euclidean Jordan algebras ⋮ Complete monotonicity for inverse powers of some combinatorially defined polynomials ⋮ A REPRESENTATION THEOREM FOR LYAPUNOV-LIKE TRANSFORMATIONS ON EUCLIDEAN JORDAN ALGEBRAS ⋮ The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences ⋮ On perturbation bounds of eigenvalues in Euclidean Jordan Algebras

Cites Work

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• Some P-properties for linear transformations on Euclidean Jordan algebras
• Geršgorin type theorems for quaternionic matrices
• Some inertia theorems in Euclidean Jordan algebras
• Extension of primal-dual interior point algorithms to symmetric cones
• Matrix representations of octonions and their applications
• The exceptional Jordan eigenvalue problem
• Lie groups in the foundations of geometry
• Matrix Analysis
• The octonions
• The octonionic eigenvalue problem
• Octonionic Hermitian matrices with non-real eigenvalues
• Quaternions and matrices of quaternions

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