Results 11 to 20 of about 8,466 (229)

Upper and Lower Bounds for Ranks of the Matrix Expression X-XAX [PDF]

Abstract and Applied Analysis, 2013
We consider the question of how to take X such that the nonlinear matrix expression X-XAX attains its maximal and minimal possible ranks.
Zhiping Xiong
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On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction

Abstract and Applied Analysis, 2014
We discuss the feasible interval of the parameter k and a general expression of matrix X which satisfies the rank equation r(A-BXC)=k. With these results, we study two problems under the rank constraint r(A-BXC)=k.
Hongxing Wang, Yeguo Sun
doaj   +2 more sources

Ranks of a Constrained Hermitian Matrix Expression with Applications

Journal of Applied Mathematics, 2013
We establish the formulas of the maximal and minimal ranks of the quaternion Hermitian matrix expression C4−A4XA4∗ where X is a Hermitian solution to quaternion matrix equations A1X=C1, XB1=C2, and A3XA3*=C3.
Shao-Wen Yu
doaj   +2 more sources

A Dichotomy Theorem for Ordinal Ranks in MSO [PDF]

Logical Methods in Computer Science
We focus on formulae $\exists X.\, φ(\vec{Y}, X)$ of monadic second-order logic over the full binary tree, such that the witness $X$ is a well-founded set.
Damian Niwiński, Paweł Parys, Michał Skrzypczak   +2 more
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The Reverse Order Law for the {1,3M,4N}—The Inverse of Two Matrix Products

Axioms
By using the maximal and minimal ranks of some generalized Schur complement, the equivalent conditions for the reverse order law (AB){1,3M,4K}=B{1,3N,4K}A{1,3M,4N} are presented.
Yingying Qin, Baifeng Qiu, Zhiping Xiong
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The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications

International Journal of Mathematics and Mathematical Sciences, 2012
We establish necessary and sufficient conditions for the existence of and the expressions for the general real and complex Hermitian solutions to the classical system of quaternion matrix equations A1X=C1,XB1=C2, and  A3XA3*=C3. Moreover, formulas of the
Shao-Wen Yu
doaj   +2 more sources

Optimization Problems of Hermitian Quadratic Matrix-Valued Functions and Applications

Axioms
In this paper, we investigate optimization problems for a Hermitian quadratic matrix-valued function involving two variable matrices. We derive algebraic formulas for the maximal and minimal ranks and partial inertias of this function based on a ...
Sihem Guerarra
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Maximal rank and minimal generation of some parametric varieties

Journal of Pure and Applied Algebra, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chiantini L., Orecchia F., Ramella I.
openaire   +3 more sources

Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation [PDF]

, 2010
The extreme ranks, i.e., the maximal and minimal ranks, are established for the general Hermitian solution as well as the general skew-Hermitian solution to the classical matrix equation AXA∗ +BY B∗ = C over the quaternion algebra.
Jing, Jiang, Wang, Qing-Wen
core   +1 more source

The maximal and minimal ranks of a quaternion matrix expression with applications

Journal of the Egyptian Mathematical Society, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rashedi, Somayeh, Ebadi, Ghodrat, Biswas, Anjan   +2 more
openaire   +1 more source