Journal
LINEAR & MULTILINEAR ALGEBRA
Volume 69, Issue 16, Pages 3069-3091Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/03081087.2019.1704213
Keywords
Sylvester generalized equation; quaternion; eta-Hermitian matrix; general solution; solvability
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Funding
- National Natural Science Foundation of China [11801354]
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This paper establishes a different approach for solving a system of quaternion matrix equations, deriving new necessary and sufficient conditions for existence of a solution and showing equivalence with previous solvability conditions. The general solution to the system is provided when the solvability conditions are met, with applications discussed including general eta-Hermitian solution.
In this paper, we establish a different approach for solving the system of three coupled two-sided Sylvester-type quaternion matrix equations . We give some new necessary and sufficient conditions for the existence of a solution to this system in terms of Moore-Penrose inverses of the matrices involved. We show that these new solvability conditions are equivalent with the solvability conditions which were presented in a recent paper [Linear Algebra Appl. 2016;496:549-593]. The general solution to the system is given when the solvability conditions are satisfied. Applications that are discussed include the solvability conditions and general eta-Hermitian solution to a system of quaternion matrix equations.
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