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Quaternions and the “Ausdehnungslehre” [PDF]
Nature, 1891 THE year 1844 is memorable in the annals of mathematics on account of the first appearance on the printed page of Hamilton's “Quaternions” and Grassmann's “Ausdehnungslehre.” The former appeared in the July, October, and supplementary numbers of the Philosophical Magazine, after a previous communication to the Royal Irish Academy, November 13, 1843 ...
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Quaternionic reduction and quaternionic orbifolds
Mathematische Annalen, 1988 On considere un processus de reduction pour des varietes de Kahler quaternioniques. On montre qu'il existe dans ce cas une certaine application impulsion qui se reduit a celle classique quand la courbure scalaire K de l'espace est zero (et les metriques deviennent hyperkahler).
Galicki, K., Lawson, H.B. Jr.
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Quaternion Hankel Transform and its Generalization [PDF]
Sahand Communications in Mathematical AnalysisIn this study, the quaternion Hankel transform is developed. Basic operational properties and inversion formula of quaternion Hankel transform are derived. Parseval’s relation for this transform is also established.
Khinal Parmar, V. R. Lakshmi Gorty
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IEEE Access, 2022 We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements.
Johannes Poppelbaum, Andreas Schwung
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The quaternionic determinant [PDF]
The Electronic Journal of Linear Algebra, 2000 The determinant for complex matrices cannot be extended to quaternionic matrices. Instead, the Study determinant and the closely related $q$-determinant are widely used. We show that the Study determinant can be characterized as the unique functional which extends the {\em absolute value} of the complex determinant and discuss its spectral and linear ...
Stefano De Leo, Nir Cohen
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Quaternionic Integrability [PDF]
Journal of Nonlinear Mathematical Physics, 2021 Standard (Arnold–Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones, and more generally by the action of a Clifford group.
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, 2018 Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices.
Enshaeifar, Shirin +6 more
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Rotacija z enotskim kvaternionom ( = Rotation with unit quaternion) [PDF]
Geodetski Vestnik, 2014 A quaternion is a hyper-complex number. A rule for quaternion multiplications allows us to use it as a rotation in three-dimensional space. The aim of this article is to present quaternion rotations to the Slovene professional geodetic public ...
Klemen Kregar +2 more
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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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