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Weighted Minimization Problems for Quaternion Matrices
Advances in Applied Clifford Algebras, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kyrchei, Ivan I. +2 more
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2020
This chapter contains some basic knowledge on quaternions, Toeplitz and Hankel matrices and we introduce some useful maps which allow to consider, instead of quaternionic matrices, complex matrices of double size. For more information about quaternionic matrices, the interested reader may consult, e.g., Rodman’s book [97]. We also recall the notions of
Daniel Alpay +2 more
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This chapter contains some basic knowledge on quaternions, Toeplitz and Hankel matrices and we introduce some useful maps which allow to consider, instead of quaternionic matrices, complex matrices of double size. For more information about quaternionic matrices, the interested reader may consult, e.g., Rodman’s book [97]. We also recall the notions of
Daniel Alpay +2 more
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SymmetryDual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion ...
Ruyu Tao, Mingcui Zhang, Musheng Wei
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Quaternionic Numerical Ranges of Normal Quaternion Matrices
AIP Conference Proceedings, 2009By the Jordan canonical block‐entry form introduced in this paper, a practical method of determining the convexity and an estimation of the location on the quaternionic numerical range are given for a normal quaternion matrix.
Feng Lianggui +3 more
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Inequalities for generalized eigenvalues of quaternion matrices
Periodica Mathematica Hungarica, 2020The paper deals with a particular generalized eigenvalue problem. It concerns a pair \(A,B\) of self-conjugate square matrices, where \(B\) is a positive definite matrix. Equivalently, this is an eigenvalue problem for the matrix \(B^{-1}A\) (see [\textit{G. W. Stewart}, Linear Algebra Appl.
Yan Hong, Feng Qi 0001
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On semigroup of quaternionic matrices
Asian-European Journal of MathematicsIn this paper, we derived some algebraic properties of matrices over the quaternions. A ∗-isomorphism between the [Formula: see text] matrices over the quaternions [Formula: see text], and a subset of the [Formula: see text] matrices [Formula: see text] over the complex numbers is established.
P. Ramesh Kumar +2 more
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Intrinsic Functions on Matrices of Real Quaternions
Canadian Journal of Mathematics, 1963It is well known that any semi-simple algebra over the real field R, or over the complex field C, is a direct sum (unique except for order) of simple algebras, and that a finite-dimensional simple algebra over a field is a total matrix algebra over a division algebra, or equivalently, a direct product of a division algebra over and a total matrix ...
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Journal of Mathematical Physics, 2004
By means of complex representation and companion vector, this paper studies the problems of eigenvalues and eigenvectors of quaternion matrices, and gives a technique of computing the eigenvalues and eigenvectors of the quaternion matrices in quaternionic quantum mechanics.
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By means of complex representation and companion vector, this paper studies the problems of eigenvalues and eigenvectors of quaternion matrices, and gives a technique of computing the eigenvalues and eigenvectors of the quaternion matrices in quaternionic quantum mechanics.
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Dual quaternion matrices and MATLAB applications
2018Summary: There are many studies in the literature on real quaternions and real quaternion matrices. There are few studies in the literature on dual quaternions. Definitions of the matrices of dual quaternions used in this study will be given. The originality of our research, the set of dual quaternion matrix we studied, will be defined for the first ...
Nalbant, Kemal Gokhan, Yuce, Salim
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Stability of Invariant Subspaces of Quaternion Matrices
Complex Analysis and Operator Theory, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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