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Determinantal Representations of the Quaternion Core Inverse and Its Generalizations

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Abstract

In this paper, we extend notions of the core inverse, core-EP inverse, DMP inverse, and CMP inverse over the quaternion skew field \({\mathbb {H}}\) that have some features in comparison to complex matrices. We give the direct method of their computing, namely, their determinantal representations by using column and row noncommutative determinants previously introduced by the author. As the special case, we give their determinantal representations for complex matrices as well. A numerical example to illustrate the main result is given.

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  1. Pidstrygach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, str. Naukova 3b, Lviv, 79060, Ukraine

    Ivan Kyrchei

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  1. Ivan Kyrchei
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Correspondence to Ivan Kyrchei.

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Communicated by G. Stacey Staples

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Kyrchei, I. Determinantal Representations of the Quaternion Core Inverse and Its Generalizations. Adv. Appl. Clifford Algebras 29, 104 (2019). https://doi.org/10.1007/s00006-019-1024-6

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