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On the Consimilarity of Split Quaternions and Split Quaternion Matrices [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations and in split quaternions and split quaternion ...
Kösal Hidayet Hüda +2 more
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Commutative Quaternion Matrices [PDF]
Advances in Applied Clifford Algebras, 2014 In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative quaternion matrices using properties of complex matrices.
Hidayet Huda Kosal +2 more
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Split quaternion matrices [PDF]
Miskolc Mathematical Notes, 2012 In this paper, we consider split quaternions and split quaternion matrices. Firstly, we give some properties of split quaternions. After that we investigate split quaternion matrices using properties of complex matrices. Then we define the complex adjoint matrix of split quaternion matrices and we describe some of their properties. Furthermore, we give
Alagöz, Yasemin +2 more
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Low Rank Pure Quaternion Approximation for Pure Quaternion Matrices [PDF]
SIAM Journal on Matrix Analysis and Applications, 2021 Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure quaternion matrix can be obtained by using the quaternion singular value decomposition.
Michael Ng +2 more
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The Commutation Matrices of Elements in Kronecker Quaternion Groups [PDF]
Jambura Journal of Mathematics, 2022 This article discusses the commutation matrix in the Kronecker quaternion group; that is, a non-abelian group whose 32 elements are matrices of 4 × 4 size, with entries in the set of complex numbers.
Yanita Yanita +2 more
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Mathematics, 2023 Let H denote the quaternion algebra. This paper investigates the generalized complementary covariance, which is the ϕ-Hermitian quaternion matrix. We give the properties of the generalized complementary covariance matrices.
Zhuo-Heng He, He Zhuo-Heng
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Elliptic Quaternion Matrices: Theory and Algorithms
AxiomsIn this study, we obtained results for the computation of eigen-pairs, singular value decomposition, pseudoinverse, and the least squares problem for elliptic quaternion matrices.
Hidayet Hüda Kösal +3 more
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Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices
Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2019 In this paper, we consider one of the most knownFibonacci matrix Qand the Fibonacciquaternion matrix MQFn, where Qnis the n-th Fibonacci quaternion.In particular we define some new quaternion matrices.
Bahar Demirtürk Bitim
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The quaternion-type cyclic-Fibonacci sequences in groups [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we define the six different quaternion-type cyclic-Fibonacci sequences and present some properties, such as, the Cassini formula and generating function. Then, we study quaternion-type cyclic-Fibonacci sequences modulo m.
Nazmiye Yilmaz +2 more
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New Insight into Quaternions and Their Matrices
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2021 The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced.
Gülsüm Yeliz ŞENTÜRK +2 more
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