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- Title
The Solvability of a System of Quaternion Matrix Equations Involving ϕ -Skew-Hermicity.
- Authors
He, Zhuo-Heng; Zhang, Xiao-Na; Zhao, Yun-Fan; Yu, Shao-Wen
- Abstract
Let H be the real quaternion algebra and H m × n denote the set of all m × n matrices over H. For A ∈ H m × n , we denote by A ϕ the n × m matrix obtained by applying ϕ entrywise to the transposed matrix A T , where ϕ is a non-standard involution of H. A ∈ H n × n is said to be ϕ -skew-Hermicity if A = − A ϕ . In this paper, we provide some necessary and sufficient conditions for the existence of a ϕ -skew-Hermitian solution to the system of quaternion matrix equations with four unknowns A i X i (A i) ϕ + B i X i + 1 (B i) ϕ = C i , (i = 1 , 2 , 3) , A 4 X 4 (A 4) ϕ = C 4 .
- Subjects
QUATERNIONS; EQUATIONS; MATRIX decomposition; MATRICES (Mathematics); ALGEBRA
- Publication
Symmetry (20738994), 2022, Vol 14, Issue 6, pN.PAG
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym14061273