Matrix Equation’s Reflexive and Anti-Reflexive Solutions over Quaternions

Matrix Equation’s Reflexive and Anti-Reflexive Solutions over Quaternions

We consider when the quaternion matrix equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>X</mi><mi>B</mi><mo>+</mo><mi>C</mi>...

Full description

Bibliographic Details
Main Authors: Xin Liu, Kaiqi Wen, Yang Zhang
Format: Article
Language:English
Published: MDPI AG 2022-12-01
Series:Symmetry
Subjects:
reflexive matrix
anti-reflexive matrix
quaternion matrix equation
real representation
Online Access:https://www.mdpi.com/2073-8994/15/1/40
Description
Summary:We consider when the quaternion matrix equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>X</mi><mi>B</mi><mo>+</mo><mi>C</mi><mi>X</mi><mi>D</mi><mo>=</mo><mi>E</mi></mrow></semantics></math></inline-formula> has a reflexive (or anti-reflexive) solution with respect to a given generalized reflection matrix. We adopt a real representation method to derive the solutions when it is solvable. Moreover, we obtain the explicit expressions of the least-squares reflexive (or anti-reflexive) solutions.
ISSN:2073-8994

Similar Items