Solution to a system of real quaternion matrix equations encompassing \(\eta\)-Hermicity

DOI10.1016/j.amc.2015.05.104zbMath1410.15034OpenAlexW1069452408MaRDI QIDQ1664284

Abdur Rehman, Zhuo-Heng He, Qing-Wen Wang

Publication date: 24 August 2018

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

Full work available at URL: https://doi.org/10.1016/j.amc.2015.05.104

zbMATH Keywords

general solutionrankMoore-Penrose inversequaternion matrixlinear matrix equation\(\eta\)-Hermitian solution

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Hermitian, skew-Hermitian, and related matrices (15B57) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (24)

An efficient real representation method for least squares problem of the quaternion constrained matrix equation AXB + CY D = E ⋮ Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation ⋮ Determinantal representations of solutions to systems of quaternion matrix equations ⋮ A constraint system of generalized Sylvester quaternion matrix equations ⋮ Compact formula for skew-symmetric system of matrix equations ⋮ A system of coupled quaternion matrix equations with seven unknowns and its applications ⋮ Cramer's rules of \(\eta \)-(skew-)Hermitian solutions to the quaternion Sylvester-type matrix equations ⋮ The \(\eta \)-anti-Hermitian solution to some classic matrix equations ⋮ Matrices over Quaternion Algebras ⋮ Direct Methods of Solving Quaternion Matrix Equation Based on STP ⋮ Centrohermitian and skew-centrohermitian solutions to the minimum residual and matrix nearness problems of the quaternion matrix equation \((AXB,DXE) = (C,F)\) ⋮ Matrix LSQR algorithm for structured solutions to quaternionic least squares problem ⋮ \( \eta \)-Hermitian solution to a system of quaternion matrix equations ⋮ Determinantal representations of solutions and Hermitian solutions to some system of two-sided quaternion matrix equations ⋮ A system of matrix equations with five variables ⋮ Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore-Penrose inverse ⋮ Optimization of a nonlinear Hermitian matrix expression with application ⋮ Cramer's rules for Sylvester quaternion matrix equation and its special cases ⋮ Inverse problems for \((R,S)\)-symmetric matrices in structural dynamic model updating ⋮ Reducible solution to a quaternion tensor equation ⋮ The general solution of quaternion matrix equation having \(\eta \)-skew-Hermicity and its Cramer's rule ⋮ Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations ⋮ Determinantal representations of solutions to systems of two-sided quaternion matrix equations ⋮ Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations

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