On the Inheritance of Some Complementarity Properties by Schur Complements

نویسندگان

  • Roman Sznajder
  • M. Seetharama Gowda
  • Jiyuan Tao
چکیده

In this paper, we consider the Schur complement of a subtransformation of a linear transformation defined on the product of two finite dimensional real Hilbert spaces, and in particular, on two Euclidean Jordan algebras. We study complementarity properties of linear transformations that are inherited by principal subtransformations, principal pivot transformations, and Schur complements.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Pseudo Schur complements, pseudo principal pivot transforms and their inheritance properties

Extensions of the Schur complement and the principal pivot transform, where the usual inverses are replaced by the Moore-Penrose inverse, are revisited. These are called the pseudo Schur complement and the pseudo principal pivot transform, respectively. First, a generalization of the characterization of a block matrix to be an M -matrix is extended to the nonnegativity of the Moore-Penrose inve...

متن کامل

Some properties on Schur complements of H-matrices and diagonally dominant matrices

In this paper, we obtain a theorem on the distribution of eigenvalues for Schur complements of H-matrices. Further, we give some properties of diagonal-Schur complements on diagonally dominant matrices and their distribution of eigenvalues. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A45; 15A48

متن کامل

Further results on H-matrices and their Schur complements

It is well-known [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246–251, [1]] that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant. Also, if a matrix is an H-matrix, then its Schur complement is an H-matrix, too [J. Liu, Y. Huang, Some properties on Schur complements of H-matrices and diag...

متن کامل

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‡…a0††P k……A=a†‡†, where a0 is the complement o...

متن کامل

Generalized Schur complements of matrices and compound matrices

In this paper, we obtain some formulas for compound matrices of generalized Schur complements of matrices. Further, we give some Löwner partial orders for compound matrices of Schur complements of positive semidefinite Hermitian matrices, and obtain some estimates for eigenvalues of Schur complements of sums of positive semidefinite Hermitian matrices.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014