A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application
Long-Sheng Liu, Qing‐Wen Wang, Mahmoud Saad Mehany
Abstract
We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves η-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.
Topics & Concepts
QuaternionSylvester equationMathematicsMatrix (chemical analysis)Type (biology)Sylvester's law of inertiaSylvester matrixApplied mathematicsAlgebra over a fieldPure mathematicsMathematical analysisSymmetric matrixGeometryEigenvalues and eigenvectorsPhysicsMaterials scienceEcologyPolynomial matrixMatrix polynomialBiologyComposite materialQuantum mechanicsPolynomialAlgebraic and Geometric AnalysisMatrix Theory and AlgorithmsMathematics and Applications