Schur Complements in Krein Spaces
نویسندگان
چکیده
منابع مشابه
Schur Complements on Hilbert Spaces and Saddle Point Systems
For any continuous bilinear form defined on a pair of Hilbert spaces satisfying the compatibility Ladyshenskaya-Babušca-Brezzi condition, symmetric Schur complement operators can be defined on each of the two Hilbert spaces. In this paper, we find bounds for the spectrum of the Schur operators only in terms of the compatibility and continuity constants. In the light of the new spectral results ...
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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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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.
متن کاملSchur Complements in C∗− Algebras
The formula (1) was first used by Schur [22], but the idea of the Schur complement goes back to Sylvester (1851), and the term Schur complement was introduced by E. Haynsworth [16]. In the beginning Schur complements were used in the theory of matrices. M.G. Krein [19] and W.N. Anderson and G.E. Trapp [4] extended the notion of Schur complements of matrices to shorted operators in Hilbert space...
متن کاملSchur Complements and Determinant Inequalities
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 ...
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ژورنال
عنوان ژورنال: Integral Equations and Operator Theory
سال: 2007
ISSN: 0378-620X,1420-8989
DOI: 10.1007/s00020-007-1523-z