Results 11 to 20 of about 1,931 (288)
Low Rank Perturbations of Quaternion Matrices [PDF]
The Electronic Journal of Linear Algebra, 2017 Low rank perturbations of right eigenvalues of quaternion matrices are considered. For real and complex matrices it is well known that under a generic rank-$k$ perturbation the $k$ largest Jordan blocks of a given eigenvalue will disappear while additional smaller Jordan blocks will remain.
Mehl, Christian, Ran, Andre C.M.
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Some properties of complex quaternion and complex split quaternion matrices [PDF]
Miskolc Mathematical Notes, 2019 The aim of this study is to investigate some properties of complex quaternion and complex split quaternion matrices. To verify this, we use 2x2 complex matrix representation of these quaternions. Moreover, we present a method to find the determinant of complex quaternion and complex split quaternion matrices.
Alagoz, Y., Ozyurt, G.
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An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications [PDF]
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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Ninety-Six Distinct Real Matrices for Representing a Quaternion Number [PDF]
Journal of Mathematics, 2020 In this paper, we investigate on the number of all possible real matrices representing a quaternion number as three 4×4 skew-symmetric matrices plus the identity matrix of order 4, and how to determine these matrices.
W. E. Ahmed
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Hadamard matrices of generalized quaternion type [PDF]
Discrete Mathematics, 1991 The work is devoted to the problem of Hadamard matrix (H.M.) construction using the group-theoretical approach. H.M. is determined as a right regular representation of matrix of an element in R, which is obtained from the group ring ZG, where G is a semi-direct product of a cyclic group of an odd order by a generalized quaternion group \(Q_ s\).
Yamada, Mieko, Mieko Yamada
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Inequalities for quaternion matrices [PDF]
, 2010 In this paper, we present the trace inequalities for the product of powers of quaternion positive semidefinite matrices by handing some inequalities which previously obtained any complex matrices.
Ulukök, Zübeyde, Türkmen, Ramazan
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Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion
Mathematics, 2023 The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing.
Jiang-Feng Chen +3 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.
Qiyuan Chen 0001, Jeffrey Uhlmann, Ke Ye
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Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System
International Journal of Applied Mathematics and Computer Science, 2023 This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen ...
Kitowski Zygmunt +2 more
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Determinantal inequalities of Hua-Marcus-Zhang type for quaternion matrices
Open Mathematics, 2021 In this paper, the authors extend determinantal inequalities of the Hua-Marcus-Zhang type for positive definite matrices to the corresponding ones for quaternion matrices.
Hong Yan, Qi Feng
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