Determinantal representations of the quaternion weighted Moore-Penrose inverse and corresponding Cramer's rule

2016/04/01 by Ivan Kyrchei, Kyrchei, Ivan
Computer Science · Mathematics · Physics and Astronomy · #11R52 #15A09 #15A18 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1604.00243

openalex publication_date 2016/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Weighted singular value decomposition (WSVD) and a representation of the weighted Moore-Penrose inverse of a quaternion matrix by WSVD have been derived. Using this representation, limit and determinantal representations of the weighted Moore-Penrose inverse of a quaternion matrix have been obtained within the framework of the theory of the noncommutative column-row determinants. By using the obtained analogs of the adjoint matrix, we get the Cramer rules for the weighted Moore-Penrose solutions of left and right systems of quaternion linear equations.

Citations

• A generalized inverse for matrices

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