Ranks of the common solution to six quaternion matrix equations

DOI10.1007/s10255-011-0083-9zbMath1304.15006OpenAlexW2047891712MaRDI QIDQ475694

Yan Zhou, Qin Zhang, Qing-Wen Wang

Publication date: 27 November 2014

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-011-0083-9

zbMATH Keywords

generalized inversequaternion matrixminimal rankmaximal ranksystem of matrix equationslinear matrix expression

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) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (8)

An efficient algorithm for the reflexive solution of the quaternion matrix equation \(AXB + CX^HD = F\) ⋮ The optimization on ranks and inertias of a quadratic Hermitian matrix function and its applications ⋮ The common bisymmetric nonnegative definite solutions with extreme ranks and inertias to a pair 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 ⋮ An efficient algorithm for the generalized \((P,Q)\)-reflexive solution to a quaternion matrix equation and its optimal approximation ⋮ An inverse eigenproblem for generalized reflexive matrices with normal $k+1$-potencies ⋮ Iterative algorithm for solving a class of quaternion matrix equation over the generalized \((P, Q)\)-reflexive matrices

Cites Work

• Unnamed Item
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• The matrix equations \(AX=C\), \(XB=D\)
• The common solution to matrix equations over a regular ring with applications
• Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications
• A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
• Ranks and the least-norm of the general solution to a system of quaternion matrix equations
• On the matrix equation \(AX=B\) with applications to the generators of a controllability matrix
• A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
• Upper and lower bounds for ranks of matrix expressions using generalized inverses
• Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application
• The common solution to six quaternion matrix equations with applications
• Ranks of solutions of the linear matrix equation \(AX + YB = C\)
• \(P\)-(skew)symmetric common solutions to a pair of quaternion matrix equations
• Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications
• Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
• The general solution to a system of real quaternion matrix equations
• A system of four matrix equations over von Neumann regular rings and its applications
• The solvability of two linear matrix equations
• Fiber Cone of Codimension 2 Lattice Ideals
• Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications
• Ranks of Solutions of the Matrix Equation AXB = C
• The Minimum Rank of a 3 × 3 Partial Block Matrix

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