Some inertia theorems in Euclidean Jordan algebras

DOI10.1016/j.laa.2008.11.015zbMath1168.15003OpenAlexW2036048894MaRDI QIDQ1014464

M. Seetharama Gowda, Jiyuan Tao, Melania M. Moldovan

Publication date: 29 April 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.2008.11.015

zbMATH Keywords

inertiaSylvester's law of inertiaLyapunov transformationEuclidean Jordan algebracone spectrumquadratic representationOstrowski-Schneider inertia theorem

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Simple, semisimple Jordan algebras (17C20) Finite-dimensional structures of Jordan algebras (17C55)

Related Items (28)

Solvability based on E-property for the nonlinear symmetric cone complementarity problem ⋮ The Araki-Lieb-Thirring inequality and the Golden-Thompson inequality in Euclidean Jordan algebras ⋮ Schur complements, Schur determinantal and Haynsworth inertia formulas in Euclidean Jordan algebras ⋮ Some majorization inequalities in Euclidean Jordan algebras ⋮ On the completely-Q property for linear transformations on Euclidean Jordan algebras ⋮ The minimax principle and related topics in the Jordan setting ⋮ A note on the Ostrowski-Schneider type inertia theorem in Euclidean Jordan algebras ⋮ A generalization of the Craig-Sakamoto theorem to Euclidean Jordan algebras ⋮ Minimum eigenvalue inequalities for \(Z\)-transformations on proper and symmetric cones ⋮ A new Jacobian-like method for the polyhedral cone-constrained eigenvalue problem ⋮ More results on Schur complements in Euclidean Jordan algebras ⋮ Some inequalities involving determinants, eigenvalues, and Schur complements in Euclidean Jordan algebras ⋮ Sparse recovery on Euclidean Jordan algebras ⋮ Similarity automorphism invariance of some P-properties of linear transformations on Euclidean Jordan algebras ⋮ STEIN LINEAR PROGRAMS OVER SYMMETRIC CONES ⋮ Improved complexity analysis of full Nesterov-Todd step feasible interior-point method for symmetric optimization ⋮ Improved smoothing Newton methods for symmetric cone complementarity problems ⋮ Spectral analysis of coupled linear complementarity problems ⋮ Complementarity properties of the Lyapunov transformation over symmetric cones ⋮ Lyapunov-type least-squares problems over symmetric cones ⋮ A nonsmooth algorithm for cone-constrained eigenvalue problems ⋮ Feasibility and solvability of Lyapunov-type linear programming over symmetric cones ⋮ A new class of smoothing complementarity functions over symmetric cones ⋮ On minimal rank solutions to symmetric Lyapunov equations in Euclidean Jordan algebra ⋮ The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences ⋮ Strict diagonal dominance and a Geršgorin type theorem in Euclidean Jordan algebras ⋮ On perturbation bounds of eigenvalues in Euclidean Jordan Algebras ⋮ On the finiteness of the cone spectrum of certain linear transformations on Euclidean Jordan algebras

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