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Journal of Applied Mathematics and Computing

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01.06.2015 | Original Research

Cramer’s rules for various solutions to some restricted quaternionic linear systems

verfasst von: Guang-Jing Song, Haixia Chang, Zhongcheng Wu

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2015

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Abstract

In this paper, we show some new necessary and sufficient conditions for the existences of the generalized inverses \(A_{r_{T_{1},S_{1}}}^{(2)}\) and \(A_{l_{T_{2},S_{2}}}^{(2)}\) over the quaternion skew field by checking the nonsingularity of some matrices instead of computing the direct sum of some quaternionic vector spaces. We also derive a series of concise determinantal representations of these generalized inverses. In addition, we give some condensed Cramer’s rules for the general solutions, the least squares solutions and the approximate solutions to some restricted quaternionic systems of linear equations, respectively.

Vorheriger Artikel On Dirichlet two-point boundary value problems for the Ermakov–Painlevé IV equation

Nächster Artikel An interior-point method for -linear complementarity problem based on a trigonometric kernel function

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Titel: Cramer’s rules for various solutions to some restricted quaternionic linear systems
verfasst von: Guang-Jing Song
Haixia Chang
Zhongcheng Wu
Publikationsdatum: 01.06.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2015
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-014-0793-2

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