Taiwanese Journal of Mathematics

A System of Coupled Two-sided Sylvester-type Tensor Equations over the Quaternion Algebra

Qing-Wen Wang and Xiao Wang

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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.

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Taiwanese J. Math., Advance publication (2020), 18 pages.

First available in Project Euclid: 29 May 2020

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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.)

tensor Einstein product tensor equation quaternion algebra Moore-Penrose inverse $\eta$-Hermitian tensor


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

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