A minimum principle and estimates of the eigenvalues for Schur complements of positive semidefinite Hermitian matrices

DOI10.1016/S0024-3795(96)00595-2zbMath0885.15010MaRDI QIDQ1369351

Jianzhou Liu, L. Zhu

Publication date: 8 April 1998

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

zbMATH Keywords

inequalitieseigenvaluespositive definite matricesSchur complementinequalities for determinants

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Inequalities involving eigenvalues and eigenvectors (15A42) Hermitian, skew-Hermitian, and related matrices (15B57) Miscellaneous inequalities involving matrices (15A45)

Related Items

The Schur complements of \(\gamma\)-diagonally and product \(\gamma\)-diagonally dominant matrix and their disc separation ⋮ The improved disc theorems for the Schur complements of diagonally dominant matrices ⋮ The Schur complement of strictly doubly diagonally dominant matrices and its application ⋮ The dominant degree and disc theorem for the Schur complement of matrix ⋮ Some inequalities for eigenvalues of Schur complements of Hermitian matrices ⋮ Some Löwner partial orders of Schur complements and Kronecker products of matrices ⋮ Some inequalities for singular values and eigenvalues of generalized Schur complements of products of matrices

Cites Work

• Some inequalities for the eigenvalues of the product of positive semidefinite Hermitian matrices
• Some interlacing properties of the Schur complement of a Hermitian matrix
• Inequalities Connected with Definite Hermitian Forms, II
• Inequalities: theory of majorization and its applications
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