Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Advance publication (2020), 18 pages.
A System of Coupled Two-sided Sylvester-type Tensor Equations over the Quaternion Algebra
We establish some necessary and sufficient conditions for the solvability to a system of a pair of coupled two-sided Sylvester-type tensor equations over the quaternion algebra. We also give an expression of the general solution to the system when it is solvable. As applications, we derive some solvability conditions and expressions of the $\eta$-Hermitian solutions to some systems of coupled two-sided Sylvester-type quaternion tensor equations. Moreover, we provide an example to illustrate the main results of this paper.
Taiwanese J. Math., Advance publication (2020), 18 pages.
First available in Project Euclid: 29 May 2020
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Digital Object Identifier
Primary: 11R52: Quaternion and other division algebras: arithmetic, zeta functions 15A09: Matrix inversion, generalized inverses 15A24: Matrix equations and identities 15A69: Multilinear algebra, tensor products 15B33: Matrices over special rings (quaternions, finite fields, etc.)
Wang, Qing-Wen; Wang, Xiao. A System of Coupled Two-sided Sylvester-type Tensor Equations over the Quaternion Algebra. Taiwanese J. Math., advance publication, 29 May 2020. doi:10.11650/tjm/200504. https://projecteuclid.org/euclid.twjm/1590717619