The \((P,Q)\)-(skew)symmetric extremal rank solutions to a system of quaternion matrix equations

DOI10.1016/j.amc.2011.04.011zbMath1222.15022OpenAlexW1977502914MaRDI QIDQ548004

Qin Zhang, Qing-Wen Wang

Publication date: 27 June 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.04.011

zbMATH Keywords

numerical exampleMoore-Penrose inversequaternion algebraminimal rankmaximal ranksystem of quaternion matrix equations\((P,Q)\)-skewsymmetric matrix\((P,Q)\)-symmetric matrixextremal rank solutions

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)

Related Items

The optimization on ranks and inertias of a quadratic Hermitian matrix function and its applications ⋮ The general solutions to some systems of matrix equations ⋮ The \(\{P, Q, k + 1 \}\)-reflexive solution to system of matrix equations \(A X = C\), \(X B = D\) ⋮ On the Hermitian structures of the solution to a pair of matrix equations ⋮ Solvability of systems of linear matrix equations subject to a matrix inequality ⋮ Some structures of submatrices in solution to the paire of matrix equations \(AX=C,XB=D\) ⋮ The common bisymmetric nonnegative definite solutions with extreme ranks and inertias to a pair of matrix equations ⋮ Inertias and ranks of some Hermitian matrix functions with applications ⋮ Constrained solutions of a system of matrix equations ⋮ (Anti-)Hermitian generalized (anti-)Hamiltonian solution to a system of matrix equations ⋮ The generalized bisymmetric (bi-skew-symmetric) solutions of a class of matrix equations and its least squares problem ⋮ A quick exponentiation algorithm for \(3\times 3\) block upper triangular matrices ⋮ Inverse problems for \((R,S)\)-symmetric matrices in structural dynamic model updating

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The matrix equations \(AX=C\), \(XB=D\)
• Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications
• Quaternion singular value decomposition based on bidiagonalization to a real or complex matrix using quaternion Householder transformations
• A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
• The generalized reflexive solution for a class of matrix equations \( (AX=B, XC=D)\)
• Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing
• On the matrix equation \(AX=B\) with applications to the generators of a controllability matrix
• Minimum norm regularization of descriptor systems by mixed output feedback
• The spectral theorem in quaternions
• The reflexive and anti-reflexive solutions of the matrix equation \(AX=B\).
• The maximal and minimal ranks of \(A - BXC\) with applications
• Inverse eigenproblems and associated approximation problems for matrices with generalized symmetry or skew symmetry.
• Two matrix-based proofs that the linear estimator \(G y\) is the best linear unbiased estimator
• Minimization problems for \((R,S)\)-symmetric and \((R,S)\)-skew symmetric matrices
• The matrix equations \(AX=B, XC=D\) with \(PX= sXP\) constraint
• \(P\)-(skew)symmetric common solutions to a pair of quaternion matrix equations
• Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
• The general solution to a system of real quaternion matrix equations
• On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model
• Nonnegative definite and positive definite solutions to the matrix equationAXA^*=B
• PARTIALLY SUPERFLUOUS OBSERVATIONS
• Regularization of Singular Systems by Derivative and Proportional Output Feedback
• Generalized Reflexive Matrices: Special Properties and Applications
• Right eigenvalue equation in quaternionic quantum mechanics
• Hypercomplex correlation techniques for vector images
• Quaternions and matrices of quaternions