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Commutative Quaternion Matrices [PDF]
Advances in Applied Clifford Algebras, 2013 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.
Kösal, Hidayet Hüda, Tosun, Murat
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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.
Guangjing Song +2 more
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Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
Special Matrices, 2014 L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331(2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformationsA ↦ ˜S−1AS in which S is a nonsingular quaternion matrix ...
Klimchuk Tatiana, Sergeichuk Vladimir V.
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An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
Journal of Applied Mathematics, 2014 This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices.
Tongsong Jiang, Xuehan Cheng, Sitao Ling
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Creating 3, 4, 6 and 10-dimensional spacetime from W3 symmetry [PDF]
Physics Letters B, 2017 We describe a model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four “magical” Jordan algebras of 3×3 ...
J. Ambjørn, Y. Watabiki
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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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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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The Commutation Matrices of Elements in Kronecker Quaternion Groups
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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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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Generalizing Frobenius inversion to quaternion matrices
Numerical Algorithms, 2023 Abstract In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient that other existing methods.
Chen, Qiyuan, Uhlmann, Jeffrey, Ye, Ke
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