Similarity and consimilarity of hyper‐dual generalized quaternions

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-17 DOI:10.1002/mma.10488

Yasemin Alagöz, Gözde Özyurt

引用次数: 0

Abstract

The aim of this paper is to investigate similarity and consimilarity of hyper‐dual generalized quaternions and their matrices. For this purpose, we give different conjugates according to the generalized quaternionic units . We present ‐consimilarity of hyper‐dual generalized quaternions and their matrices except hyper‐dual ‐quaternions. For the generalization consisting of hyper‐dual coefficients quaternion and split quaternion, we search ‐consimilarity and ‐consimilarity with the help of ‐conjugate and ‐conjugate. We also give ‐coneigenvalues and ‐coneigenvectors of the matrices of these generalizations. In addition, we examine right coneigenvalue problem in generalized quaternion matrices for real and split quaternions. The complex matrix representation obtained through the complex adjoint matrix representation of this generalization is introduced, and its properties are presented. Besides, we give algebraic methods for the concept of right coneigenvalues and coneigenvectors for matrices, which are the generalization of real quaternion and split quaternion.

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超二元广义四元数的相似性和相通性

本文旨在研究超二元广义四元数及其矩阵的相似性和相通性。为此，我们根据广义四元数单位给出了不同的共轭。除了超二元四元数之外，我们还提出了超二元广义四元数及其矩阵的-相似性。对于由超二元系数四元数和分裂四元数组成的广义四元数，我们借助-共轭和-共轭来搜索-相似性和-相似性。我们还给出了这些广义矩阵的-锥特征值和-锥特征向量。此外，我们还研究了实四元数和分裂四元数的广义四元数矩阵的右锥特征值问题。我们介绍了通过这种广义的复邻接矩阵表示而得到的复矩阵表示，并介绍了它的性质。此外，我们还给出了实四元数和分裂四元数广义矩阵的右锥特征值和锥特征向量概念的代数方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.