Results 11 to 20 of about 1,238 (267)
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.
Ran, André, Mehl, Chr.
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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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Some New Properties of The Real Quaternion Matrices and Matlab Applications
Cumhuriyet Science Journal, 2019 In this study, firstly, it was shown that the set of real quaternionmatrices is a -dimensional module over the real matrix ring and -dimensional module over the complex matrix ring .
Kemal Gökhan Nalbant, Salim Yüce
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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 +2 more
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Right linear map preserving the left spectrum of 2x2 quaternion matrices; pp. 378–386 [PDF]
Proceedings of the Estonian Academy of Sciences, 2018 In this paper, the form of a right linear map preserving the left spectrum of quaternion matrices of order 2 is characterized. The obtained conclusion is different from the classical results of the linear map preserving eigenvalues of complex matrices.
Deyu Duan +3 more
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Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity, semisimilarity, and consemisimilarity over the commutative quaternion algebra and commutative quaternion ...
Kosal Hidayet Huda, Tosun Murat
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On the Consimilarity of Split Quaternions and Split Quaternion Matrices
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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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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Quaternion feedback attitude control system design based on weighted–L2–gain performance
Results in Engineering, 2023 The operation and accomplishment of a satellite's mission depend on its capacity to control its attitude. A rotation matrix parameterization, such as a (unit) quaternion, is frequently used to represent the attitude information needed for attitude ...
Harry Septanto +2 more
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Abstract and Applied Analysis, 2013 The matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F, which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory.
Ning Li, Qing-Wen Wang
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