Schur complements, Schur determinantal and Haynsworth inertia formulas in Euclidean Jordan algebras

DOI10.1016/j.laa.2009.11.015zbMath1264.15014OpenAlexW2007037775MaRDI QIDQ846306

M. Seetharama Gowda, Roman Sznajder

Publication date: 9 February 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.11.015

zbMATH Keywords

Euclidean Jordan algebrasSchur complementquaternionsoctonionsHaynsworth inertia formulaSchur determinantal formula

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Jordan algebras (algebras, triples and pairs) (17C99)

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Cites Work

• Unnamed Item
• Some P-properties for linear transformations on Euclidean Jordan algebras
• Finiteness conditions in Jordan pairs
• Schur complements, Schur determinantal and Haynsworth inertia formulas in Euclidean Jordan algebras
• Some inertia theorems in Euclidean Jordan algebras
• Strict diagonal dominance and a Geršgorin type theorem in Euclidean Jordan algebras
• What are Schur complements, anyway?
• Schur complements and statistics
• On transformations and determinants of Wishart variables on symmetric cones
• Extension of primal-dual interior point algorithms to symmetric cones
• The Schur complement and its applications
• Matrix Analysis
• On manifestations of the Schur complement
• The quaternionic determinant
• The octonionic eigenvalue problem