Results 11 to 20 of about 19,319 (303)
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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Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators [PDF]
, 2019 This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies.
Heitor J. Savino +3 more
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RKHS Representations for Augmented Quaternion Random Signals: Application to Detection Problems
Mathematics, 2022 The reproducing kernel Hilbert space (RKHS) methodology has shown to be a suitable tool for the resolution of a wide range of problems in statistical signal processing both in the real and complex domains.
Antonia Oya
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Generalised quadratic forms and the u-invariant [PDF]
, 2017 The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in characteristic 2 and
Dolphin, Andrew
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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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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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Quaternion quadratic equations in characteristic 2 [PDF]
, 2014 In this paper we present a solution for any standard quaternion quadratic equation, i.e. an equation of the form $z^2+\mu z+\nu=0$ where $\mu$ and $\nu$ belong to some quaternion division algebra $Q$ over some field $F$, assuming the characteristic of $F$
Chapman, Adam
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Quaternion Algebras and the Algebraic Legacy of Hamilton's Quaternions [PDF]
Irish Mathematical Society Bulletin, 2006 We describe the basic definitions and fundamen- tal properties of quaternion algebras over fields and proceed to give an account of how Hamilton's 1843 discovery of the quaternions was a major turning point in the subject of al- gebra. Noncommutative algebra started here! We will em- phasize especially the theory of division algebras and other kinds of
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Axioms, 2023 Quaternion is a four-dimensional and an extension of the complex number system. It is often viewed from various fields, such as analysis, algebra, and geometry.
Alit Kartiwa +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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