On Balancing and Lucas-balancing Quaternions

Patel, Bijan Kumar

doi:10.2478/cm-2021-0010

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The Balancing Split Quaternions and Lucas-balancing Split Qu...1

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2024

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Cited by 3 publications

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“…where P n and PL n are the nth Pell and Pell-Lucas number, respectively. In [22,23], balancing quaternions, Lucas-balancing quaternions, and some generalizations of these quaternions were considered. Inspired by these results, we introduce balancing split quaternions and Lucas-balancing split quaternions and present some properties of these split quaternions.…”

Section: The Balancing Split Quaternions and Lucas-balancing Split Qu...mentioning

confidence: 99%

On Some Combinatorial Properties of Balancing Split Quaternions

Bród

2024

Symmetry

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Quaternions and split quaternions are used in quantum physics, computer science, and in many areas of mathematics. In this paper, we define and study two new classes of split quaternions, namely balancing split quaternions and Lucas-balancing split quaternions. Moreover, well-known properties, e.g., Catalan, d’Ocagne, and Vajda identities, for these quaternions are also presented. We give matrix generators for balancing split quaternions and Lucas-balancing split quaternions, too.

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Section: The Balancing Split Quaternions and Lucas-balancing Split Qu...mentioning

confidence: 99%