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Journal of Applied Mathematics and Computing

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01-03-2013 | Applied mathematics

Bott-Duffin inverse over the quaternion skew field with applications

Author: Guang-Jing Song

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2013

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Abstract

In this paper, we show some properties of the Bott-Duffin inverses \(A_{r_{ ( L_{1} ) }}^{ ( -1 ) }\) and \(A_{l_{ ( L_{2} ) }}^{ ( -1 ) }\) over the quaternion skew field. In particular, we establish the determinantal representations of these generalized inverses by the theory of the column and row determinants. Moreover, we derive some Cramer rules for the unique solution to some restricted linear quaternion equations. The findings of this paper extend some known results in the literature.

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Title: Bott-Duffin inverse over the quaternion skew field with applications
Author: Guang-Jing Song
Publication date: 01-03-2013
Publisher: Springer-Verlag
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2013
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-012-0614-4

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