The solutions of the quaternion matrix equation \(AX^\varepsilon + BX^\delta = 0\)

DOI10.1016/j.laa.2023.08.021zbMath1525.65035OpenAlexW4386414595MaRDI QIDQ6083993

Publication date: 31 October 2023

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2023.08.021

zbMATH Keywords

solution space Kronecker canonical form quaternion generalized Sylvester equation involutive automorphism and anti-automorphism

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Numerical methods for matrix equations (65F45)

Cites Work

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The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits
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Some matrix equations over a finite field
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The solutions to matrix equation \(AX=B\) with some constraints
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The solution of the equation \(AX + X^{\star}B =0\)
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The solution to matrix equation \(AX+X^TC=B\)
Generalization of Roth's solvability criteria to systems of matrix equations
An efficient algorithm for the reflexive solution of the quaternion matrix equation \(AXB + CX^HD = F\)
On a solution of the quaternion matrix equation \(X-A \widetilde{X} B=C\) and its application
The solution of the equationAX + BX^⋆ = 0
The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E
Coupled Sylvester-type Matrix Equations and Block Diagonalization

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