Explicit determinantal formulas for solutions to the generalized Sylvester quaternion matrix equation and its special cases

2018/09/21 by Ivan Kyrchei, Kyrchei, Ivan
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.1809.08322

Abstract

Within the framework of the theory of quaternion column-row determinants and using determinantal representations of the Moore-Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of solutions (analogs of Cramer's rule) to the quaternion two-sided generalized Sylvester matrix equation \bf A₁\bf X₁\bf B₁+ \bf A₂\bf X₂\bf B₂=\bf C and its all special cases when its first term or both terms are one-sided. Finally, we derive determinantal representations of two like-Lyapunov equations.

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