Results 11 to 20 of about 3,462 (293)
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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Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales
Open Mathematics, 2020 In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex ...
Li Zhien, Wang Chao
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Reachability problems in quaternion matrix and rotation semigroups [PDF]
Information and Computation, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul Bell, Igor Potapov
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Novel quaternion matrix factorisations [PDF]
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016 The recent introduction of η-Hermitian matrices A = AηH has opened a new avenue of research in quaternion signal processing. However, the exploitation of this matrix structure has been limited, perhaps due to the lack of joint diagonalisation methodologies of these matrices.
Shirin Enshaeifar +3 more
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A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation [PDF]
Abstract and Applied Analysis, 2014 A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equation X−AX^B=CY based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient
Caiqin Song +3 more
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Solution to Several Split Quaternion Matrix Equations
MathematicsSplit quaternions have various applications in mathematics, computer graphics, robotics, physics, and so on. In this paper, two useful, real representations of a split quaternion matrix are proposed. Based on this, we derive their fundamental properties.
Xin Liu, Tong Shi, Yang Zhang
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Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations
Journal of MathematicsIn this article, we use the real representation matrix of the split quaternion matrix, vector operator, Kronecker product, and Moore–Penrose generalized inverse.
Yang Zhang, Xiaoda Zhang
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The Hoffman-Wielandt inequality for quaternion matrices and quaternion matrix polynomials
Mathematical Inequalities & ApplicationsThe purpose of this paper is to derive the Hoffman-Wielandt inequality and its generalization for quaternion matrices. Diagonalizability of the block companion matrix of certain quadratic (linear) quaternion matrix polynomials is brought out. As a consequence, we prove that if $Q(λ)$ is another quadratic (linear) quaternion matrix polynomial, then ...
Basavaraju, Pallavi +2 more
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Algebraic Techniques for Canonical Forms and Applications in Split Quaternionic Mechanics
Journal of Mathematics, 2023 The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical
Tongsong Jiang +4 more
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Color face recognition using quaternion PCA [PDF]
, 2011 Recently, biometric systems have attracted the attention of both academic and industrial communities. Advances in hardware and software technologies have paved the way to such growing interest.
Jaha, Emad Sami +3 more
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