Results 21 to 30 of about 666,240 (259)
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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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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The images of noncommutative polynomials evaluated on the quaternion algebra [PDF]
, 2019 Let $p$ be a multilinear polynomial in several non-commuting variables with coefficients in an arbitrary field $K$. Kaplansky conjectured that for any $n$, the image of $p$ evaluated on the set $M_n(K)$ of $n$ by $n$ matrices is a vector space.
S. Malev
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Quaternion Algebras and Generalized Fibonacci–Lucas Quaternions [PDF]
Advances in Applied Clifford Algebras, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flaut, Cristina, Savin, Diana
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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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Some Results On Quaternion 3-Space
Cumhuriyet Science Journal, 2018 In this paper, the set J′=H(Q₄,Jγ) of 4 by 4 matrices, withentries in a quaternion F-algebra Q, that are symmetric with respect to thecanonical involution Jγ is studied.
Atilla Akpınar, Fatma Özen Erdoğan
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IEEE Access, 2023 The processing of color images is of great interest, because the human perception of color is a very complex process, still not well understood. In this article, firstly the authors present an analysis of the well-known mathematical methods used to model
Eduardo Bayro-Corrochano +2 more
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Curvilinear integral theorem for $G$-monogenic mappings in the algebra of complex quaternion [PDF]
, 2016 For $G$-monogenic mappings taking values in the algebra of complex quaternion we prove a curvilinear analogue of the Cauchy integral theorem in the case where a curve of integration lies on the boundary of a domain.Comment: submitted to International ...
Kuzmenko, T. S.
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A Convolution Theorem Related to Quaternion Linear Canonical Transform
Abstract and Applied Analysis, 2019 We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion convolution in the QLCT domain
Mawardi Bahri, Ryuichi Ashino
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Enabling quaternion derivatives: the generalized HR calculus [PDF]
Royal Society Open Science, 2015 Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective
Dongpo Xu +3 more
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