Results 221 to 230 of about 12,285 (254)

On Complex Split Quaternion Matrices

Advances in Applied Clifford Algebras, 2013
Soon 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 Matrix Representation of Dual Split Quaternions and Their Matrices

Advances in Applied Clifford Algebras, 2015
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Erdoğdu, Melek, Özdemir, Mustafa
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Split quaternion nonlinear adaptive filtering

Neural Networks, 2010
A 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, Clive Cheong, Took, Danilo P, Mandic   +2 more
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A complex structure-preserving algorithm for split quaternion matrix LDU decomposition in split quaternion mechanics

Calcolo, 2021
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Gang Wang, Tongsong Jiang, Zhenwei Guo, Dong Zhang   +3 more
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On Eigenvalues of Split Quaternion Matrices

Advances in Applied Clifford Algebras, 2013
A method for finding left eigenvalues of split quaternion matrices is established. Existence of right eigenvalues of a split quaternion matrix satisfying some equation is proved. The authors also show that the Gershgorin theorem which provides an inclusion disc for left eigenvalues of quaternion matrices also holds for split quaternion matrices.
Erdoğdu, Melek, Özdemir, Mustafa
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Algebraic techniques for eigenvalues and eigenvectors of a split quaternion matrix in split quaternionic mechanics

Computer Physics Communications, 2018
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Tongsong Jiang, Zhaozhong Zhang, Ziwu Jiang   +2 more
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On singular value decomposition for split quaternion matrices and applications in split quaternionic mechanics

Journal of Computational and Applied Mathematics
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Gang Wang, Tongsong Jiang, V.I. Vasil’ev, Zhenwei Guo   +3 more
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A note on quaternion matrices and split quaternion matrix pencils

Journal of Applied Mathematics and Computing, 2017
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Cramer’s rule over quaternions and split quaternions: A unified algebraic approach in quaternionic and split quaternionic mechanics

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, Zhang, Dong, Guo, Zhenwei, Jiang, Tongsong   +3 more
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Split Fibonacci Quaternions

Advances in Applied Clifford Algebras, 2013
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Akyiğit, Mahmut, Tosun, Murat, Kösal, Hidayet Hüda   +2 more
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