Results 211 to 220 of about 8,275 (244)
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Split Pell and Pell–Lucas Quaternions
Advances in Applied Clifford Algebras, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ümit Tokeşer +2 more
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Involutions in Dual Split-Quaternions
Advances in Applied Clifford Algebras, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bekar, MURAT, Yayli, Yusuf
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Journal of Algebra and Its Applications, 2020
This paper aims to present, in a unified manner, Cramer’s rule which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies Cramer’s rule for the system of v-quaternionic linear equations by means of a complex matrix representation of v-quaternion matrices, and gives an algebraic ...
Wang, Gang +3 more
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This paper aims to present, in a unified manner, Cramer’s rule which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies Cramer’s rule for the system of v-quaternionic linear equations by means of a complex matrix representation of v-quaternion matrices, and gives an algebraic ...
Wang, Gang +3 more
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On Hyperbolic Split Quaternions and Hyperbolic Split Quaternion Matrices
Advances in Applied Clifford Algebras, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Özyurt, Gözde, ALAGÖZ, Yasemin
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Split Quaternion Matrix Representation of Dual Split Quaternions and Their Matrices
Advances in Applied Clifford Algebras, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Erdoğdu, Melek, Özdemir, Mustafa
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On Complex Split Quaternion Matrices
Advances in Applied Clifford Algebras, 2013Soon after Hamilton's discovery of the quaternion algebra, James Cockle introduced the so-called split quaternions: they have the same vector space but one defines \(i^2=-1\), \(j^2=k^2=1\), \(ijk=1\). Split quaternions also do not obey the commutative law, but there are divisors of zero, nilpotent elements and nontrivial idempotents. Furthermore, they
Erdoğdu, Melek, Özdemir, Mustafa
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Split quaternion nonlinear adaptive filtering
Neural Networks, 2010A split quaternion learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of three- and four-dimensional signals is proposed. The derivation takes into account the non-commutativity of the quaternion product, an aspect neglected in the derivation of the existing learning algorithms. It is shown that
Bukhari Che, Ujang +2 more
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Involutions in split semi‐quaternions
Mathematical Methods in the Applied Sciences, 2018A map is an involution (resp, anti‐involution) if it is a self‐inverse homomorphism (resp, antihomomorphism) of a field algebra. The main purpose of this paper is to show how split semi‐quaternions can be used to express half‐turn planar rotations in 3‐dimensional Euclidean spaceand how they can be used to express hyperbolic‐isoclinic rotations in 4 ...
Murat Bekar, Yusuf Yayli
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Calcolo, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gang Wang +3 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gang Wang +3 more
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Discrete Complex Analysis in Split Quaternions
Complex Analysis and Operator Theory, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ren, Guangbin, Zhu, Zeping
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