Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation. (English) Zbl 1474.15041

Kyrchei, Ivan I.

Abstr. Appl. Anal. 2019, Article ID 5926832, 14 p. (2019).

Summary: In this paper, we derive explicit determinantal representation formulas of general, Hermitian, and skew-Hermitian solutions to the generalized Sylvester matrix equation involving \(\ast\)-Hermicity \(\mathbf{AXA}^\ast + \mathbf{BYB}^\ast = \mathbf{C}\) over the quaternion skew field within the framework of the theory of noncommutative column-row determinants.

MSC:

15A24	Matrix equations and identities
15A15	Determinants, permanents, traces, other special matrix functions
15B57	Hermitian, skew-Hermitian, and related matrices
15B33	Matrices over special rings (quaternions, finite fields, etc.)

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