منابع مشابه
Some inequalities on generalized Schur complements
This paper presents some inequalities on generalized Schur complements. Let A be an n n (Hermitian) positive semide®nite matrix. Denote by A=a the generalized Schur complement of a principal submatrix indexed by a set a in A. Let A be the Moore± Penrose inverse of A and k A be the eigenvalue vector of A. The main results of this paper are: 1. k A a0P k A=a, where a0 is the complement o...
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This paper is focused on the applications of Schur complements to determinant inequalities. It presents a monotonic characterization of Schur complements in the L öwner partial ordering sense such that a new proof of the Hadamard-Fischer-Koteljanski inequality is obtained. Meanwhile, it presents matrix identities and determinant inequalities involving positive semidefinite matrices and extends ...
متن کاملSome inequalities involving determinants, eigenvalues, and Schur complements in Euclidean Jordan algebras
In this paper, using Schur complements, we prove various inequalities in Euclidean Jordan algebras. Specifically, we study analogues of the inequalities of Fischer, Hadamard, Bergstrom, Oppenheim, and other inequalities related to determinants, eigenvalues, and Schur complements.
متن کاملApplying Schur Complements for Handling
We describe a set of procedures for computing and updating an inverse representation of a large and sparse unsymmetric matrix A. The representation is built of two matrices: an easily invertible, large and sparse matrix A 0 and a dense Schur complement matrix S. An eecient heuristic is given that nds this representation for any matrix A and keeps the size of S as small as possible. Equations wi...
متن کاملEla Schur Complements and Banachiewicz - Schur Forms
Through the matrix rank method, this paper gives necessary and sufficient conditions for a partitioned matrix to have generalized inverses with Banachiewicz-Schur forms. In addition, this paper investigates the idempotency of generalized Schur complements in a partitioned idempotent matrix.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1999
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00046-4