Extreme Ranks of Real Matrices in Solution of the Quaternion Matrix Equation AXB = C with Applications

DOI10.1142/S1005386710000349zbMath1188.15016OpenAlexW2037280313MaRDI QIDQ3553730

Wei Xie, Qing-Wen Wang, Shao-Wen Yu

Publication date: 21 April 2010

Published in: Algebra Colloquium (Search for Journal in Brave)

Full work available at URL: http://www.worldscinet.com/ac/17/1702/S1005386710000349.html

zbMATH Keywords

generalized inversequaternion matrix equationminimal rankmaximal rankreal solutioncomplex solutionpure imaginary solution

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 (22)

Solving quaternion ordinary differential equations with two-sided coefficients ⋮ Extreme Ranks of a Partial Banded Block Quaternion Matrix Expression Subject to Some Matrix Equations with Applications ⋮ An efficient algorithm for the reflexive solution of the quaternion matrix equation \(AXB + CX^HD = F\) ⋮ Ranks of a constrained Hermitian matrix expression with applications ⋮ The optimization on ranks and inertias of a quadratic Hermitian matrix function and its applications ⋮ A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications ⋮ Minimal ranks of some quaternion matrix expressions with applications ⋮ The maximal and minimal ranks of a quaternion matrix expression with applications ⋮ Quaternion Two-Sided Matrix Equations with Specific Constraints ⋮ The real and complex Hermitian solutions to a system of quaternion matrix equations with applications ⋮ Analogs of Cramer's rule for the minimum norm least squares solutions of some matrix equations ⋮ The common bisymmetric nonnegative definite solutions with extreme ranks and inertias to a pair of matrix equations ⋮ On solutions of the quaternion matrix equation \(AX=B\) and their applications in color image restoration ⋮ Inertias and ranks of some Hermitian matrix functions with applications ⋮ Special least squares solutions of the quaternion matrix equation \(A X = B\) with applications ⋮ Optimization of a nonlinear Hermitian matrix expression with application ⋮ Solutions to optimization problems on ranks and inertias of a matrix function with applications ⋮ On solutions of the generalized Stein quaternion matrix equation ⋮ An efficient algorithm for the generalized \((P,Q)\)-reflexive solution to a quaternion matrix equation and its optimal approximation ⋮ Explicit determinantal representation formulas of \(W\)-weighted Drazin inverse solutions of some matrix equations over the quaternion skew field ⋮ Iterative algorithm for solving a class of quaternion matrix equation over the generalized \((P, Q)\)-reflexive matrices ⋮ Least squares pure imaginary solution and real solution of the quaternion matrix equation \(A X B + C X D = E\) with the least norm

Cites Work

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