Minimum eigenvalue inequalities for \(Z\)-transformations on proper and symmetric cones

DOI10.1016/j.laa.2012.12.042zbMath1266.15031OpenAlexW2051529893MaRDI QIDQ1947108

M. Seetharama Gowda, Jiyuan Tao

Publication date: 12 April 2013

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.12.042

zbMATH Keywords

linear transformationeigenvectorSchur complementminimum eigenvaluesymmetric cone\(Z\)-matricesLyapunov transformationEuclidean Jordan algebra\(Z\)-transformationsemi-definite coneStein transformationproduct cone

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48) Linear transformations, semilinear transformations (15A04)

Related Items

On the block norm-\(\mathbf P\) property, On the game-theoretic value of a linear transformation relative to a self-dual cone

Cites Work

• More results on Schur complements in Euclidean Jordan algebras
• On the bilinearity rank of a proper cone and Lyapunov-like transformations
• Some P-properties for linear transformations on Euclidean Jordan algebras
• Z-transformations on proper and symmetric cones
• Some inertia theorems in Euclidean Jordan algebras
• Extended M-matrices and subtangentiality
• Generalized M-matrices
• Extension of primal-dual interior point algorithms to symmetric cones
• On semidefinite linear complementarity problems
• Complementarity forms of theorems of Lyapunov and Stein, and related results
• Some results on a partition of \(Z\)-matrices
• On the \(\mathbf P\)-property of \(\mathbf Z\) and Lyapunov-like transformations on Euclidean Jordan algebras
• Positive operators and an inertia theorem
• Eigenvalue bounds for some classes of P -matrices
• A Survey onM-Matrices
• On Common Linear/Quadratic Lyapunov Functions for Switched Linear Systems
• Cross-Positive Matrices
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item