Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications DOI Creative Commons
Abdur Rehman,

Muhammad Zia Ur Rahman,

Asim Ghaffar

et al.

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(10), P. 26371 - 26402

Published: Jan. 1, 2024

<p>In applied and computational mathematics, quaternions are fundamental in representing three-dimensional rotations. However, specific types of quaternionic linear matrix equations remain few explored. This study introduces new their necessary sufficient conditions for solvability. We employ a methodology involving lemmas ranks coefficient matrices to develop novel algorithm. algorithm is validated through numerical examples, showing its applications advanced fields. In control theory, these used analyzing systems, particularly spacecraft attitude aerospace engineering arms robotics. quantum computing, model gates transformations, which important algorithms error correction, contributing the development fault-tolerant computers. signal processing, enhance multidimensional filtering noise reduction, with color image processing radar analysis. extend our include cases $ \eta $-Hermitian i-Hermitian solutions. Our work represents an advancement providing methods solving expanding practical applications.</p>

Language: Английский

Quaternion modified conjugate gradient algorithm to solve Sylvester-type quaternion matrix equations with generalized coupled form as well as application DOI
Yifen Ke,

Xiaomin Cai,

Riwei Liao

et al.

Applied Mathematics and Computation, Journal Year: 2025, Volume and Issue: 495, P. 129330 - 129330

Published: Jan. 30, 2025

Language: Английский

Citations

1
An $ \eta $-Hermitian solution to a two-sided matrix equation and a system of matrix equations over the skew-field of quaternions DOI Creative Commons
Mahmoud Saad Mehany, Abdullah K. Alanazi

AIMS Mathematics, Journal Year: 2025, Volume and Issue: 10(4), P. 7684 - 7705

Published: Jan. 1, 2025

Language: Английский

Citations

0
An Analysis to Some Systems of Matrix Equations with $${\phi }$$-Hermitian Solutions for Some Nonstandard Involution $${\phi }$$ Over the Real Quaternion Algebra DOI
Mahmoud Saad Mehany

Deleted Journal, Journal Year: 2025, Volume and Issue: unknown

Published: Jan. 23, 2025

Language: Английский

Citations

0
Systems of quaternionic linear matrix equations: solution, computation, algorithm, and applications DOI Creative Commons
Abdur Rehman,

Muhammad Zia Ur Rahman,

Asim Ghaffar

et al.

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(10), P. 26371 - 26402

Published: Jan. 1, 2024

<p>In applied and computational mathematics, quaternions are fundamental in representing three-dimensional rotations. However, specific types of quaternionic linear matrix equations remain few explored. This study introduces new their necessary sufficient conditions for solvability. We employ a methodology involving lemmas ranks coefficient matrices to develop novel algorithm. algorithm is validated through numerical examples, showing its applications advanced fields. In control theory, these used analyzing systems, particularly spacecraft attitude aerospace engineering arms robotics. quantum computing, model gates transformations, which important algorithms error correction, contributing the development fault-tolerant computers. signal processing, enhance multidimensional filtering noise reduction, with color image processing radar analysis. extend our include cases $ \eta $-Hermitian i-Hermitian solutions. Our work represents an advancement providing methods solving expanding practical applications.</p>

Language: Английский

Citations

0