Results 291 to 300 of about 653,122 (340)

On quaternion algebras

Journal of Mathematical Sciences, 1995
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The Algebraic Riccati Equation for Quaternions

Advances in Applied Clifford Algebras, 2013
The paper studies a Riccati equation \[ p(x):=a+bx+xc+xdx=0,\qquad a,b,c,d,x \in \mathbb{H}, \] where \(p\) is a quaternionic polynomial, which is shown to be reducible to a one-sided type. The set of quaternions \( \mathbb{H}\) can be seen as the four-dimensional vector space \( \mathbb{R}^4\) equipped with a special multiplication rule.
Janovská, Drahoslava, Opfer, Gerhard
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An Embedding Theorem for Quaternion Algebras

Journal of the London Mathematical Society, 1999
We prove an integral version of a classical embedding theorem concerning quaternion algebras \(B\) over a number field \(k\). Assume \(B\) satisfies the Eichler condition, i.e. that some infinite place of \(k\) is not ramified in \(B\), and let \(\Omega\) be an order in a quadratic extension of \(k\). We determine which maximal orders of \(B\) admit an
Chinburg, Ted, Friedman, Eduardo
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Iterative inverse kinematics for robot manipulators using quaternion algebra and conformal geometric algebra

Meccanica (Milano. Print), 2022
L. Lechuga-Gutiérrez, E. Macias-Garcia, G. Martinez-Teran, J. Zamora-Esquivel, E. Bayro-Corrochano   +4 more
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The algebra of quaternions

2014
This chapter concerns (scalar) quaternions and the basic properties of quaternion algebra, with emphasis on solution of equations such as axb = c and ax − xb =
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Kinematic equations of Lorentzian magnetic flux tubes based on split quaternion algebra

The European Physical Journal Plus, 2021
Zehra Özdemir, O. O. Tuncer, I. Gök
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Commutative quaternion algebra and DSP fundamental properties: Quaternion convolution and Fourier transform

Signal Processing, 2022
A. Grigoryan, S. Agaian
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Quaternion Nuclear Norm Minus Frobenius Norm Minimization for color image reconstruction

Pattern Recognition
Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the ...
Yu Guo, Guoqing Chen, Tieyong Zeng, Qiyu Jin, Michael Kwok-Po Ng   +4 more
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The Lengths of the Quaternion and Octonion Algebras

Journal of Mathematical Sciences, 2017
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Guterman, Alexander E., Kudryavtsev, D. K.   +1 more
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Algebras, Quaternions and Quaternionic Symplectic Groups

2002
In this chapter we begin by studying algebras over a field, with their groups of units providing many interesting groups. In particular, we study division algebras and their linear algebra. Then we introduce the quaternions which form the only non-commutative example of a real division algebra.
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