Results 31 to 40 of about 13,019 (252)
Quaternion Electromagnetism and the Relation with Two-Spinor Formalism
Universe, 2019 By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely.
In Ki Hong, Choong Sun Kim
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Bounds on the levels of composition algebras [PDF]
, 2010 Certain families of quaternion and octonion algebras are conjectured to be of level and sublevel n. A proof of this conjecture is offered in the case where n is a power of two. Hoffmann's proof of the existence of infinitely many new values for the level
James O'Shea +2 more
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An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications
Journal of Applied Mathematics, 2014 This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices.
Tongsong Jiang, Xuehan Cheng, Sitao Ling
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Machines, 2022 This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function ...
Kazuhiko Takahashi +2 more
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Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers
Journal of Mathematics, 2023 In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
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Levels and sublevels of composition algebras [PDF]
, 2007 Lewis' and Leep's bounds on the level and sublevel of quaternion algebras are extended to the class of composition algebras. Some simple constructions of composition algebras of known level values are given.
O'Shea, James
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Alexandria Engineering Journal, 2020 In this work, we continue our study of autonomous nonlinear dynamical systems with quaternion variables. We present a novel chaotic Chen system with quaternion variables. This system in real form is high (nine) dimensional.
Emad E. Mahmoud +2 more
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Quaternion lattices and quaternion fields
Archiv der Mathematik, 2023 AbstractLet $$Q_8$$ Q 8 be the quaternion group of order 8 and $${\chi }$$ χ its faithful irreducible character. Then $${\chi }$$ χ can be realized over certain imaginary quadratic number ...
openaire +2 more sources