Upper and lower bounds for ranks of the matrix expression \(X-XAX\)
type: Item
instance of: scholarly article
title: Upper and lower bounds for ranks of the matrix expression \(X-XAX\)
zbMATH Open document ID: 1291.15011
DOI: 10.1155/2013/267035
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: We consider the question of how to take \(X\) such that the nonlinear matrix expression \(X-XAX\) attains its maximal and minimal possible ranks.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 6306578
Wikidata QID: Q58915733
author: Zhiping Xiong
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/267035
OpenAlex ID: W1489404924
cites work: Q5849795
cites work: Q4061081
cites work: The Equations ATX\pm XTA=B
cites work: Q3831127
cites work: Q3789693
cites work: Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
cites work: On the solution of equality constrained quadratic programming problems arising in optimization
cites work: Minimum rank completions
cites work: The maximal and minimal ranks of some expressions of generalized inverses of matrices
cites work: Extremal Ranks of Some Symmetric Matrix Expressions with Applications
cites work: Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method
cites work: Minimal rank completions for block matrices
cites work: On the inverse of a special Schur complement
cites work: Inertias and ranks of some Hermitian matrix functions with applications
cites work: Upper and lower bounds for ranks of matrix expressions using generalized inverses
cites work: The maximal and minimal ranks of \(A - BXC\) with applications
cites work: An alternative representation of the generalized inverse of partitioned matrices
cites work: Q4050723
Recommended article: Upper and lower bounds for the rank of the matrix-valued function when X has a fixed rank
Recommended article: Upper and lower bounds for ranks of matrix expressions using generalized inverses
Recommended article: On lower and upper bounds of matrices
Recommended article: Q3676271
Recommended article: The extremal ranks of \(A_1-B_1XC_1\) subject to a pair of matrix equations
Recommended article: The lower bounds for the rank of matrices and some sufficient conditions for nonsingular matrices
Recommended article: Extremal ranks of matrix expression of \(A - BXC\) with respect to Hermitian matrix
Recommended article: The maximal and minimal ranks of matrix expression with applications
Recommended article: The minimal rank of the matrix expression \(A-BX-YC\)
Recommended article: Lower bounds for some matrices
description: scientific article; zbMATH DE number 6306578