Polar Decomposition of Complexified Quaternions and Octonions
نویسندگان
چکیده
منابع مشابه
Quaternions and Octonions in Mechanics
In fact, this group is Spin(3), the 2-fold cover of SO(3), the group of rotations of R. This has been known for quite some time and is perhaps the simplest realization of Hamilton’s expectations about the potential of quaternions for physics. One reason for the renewed interest is the fact that the resulting substitution of matrices by quaternions speeds up considerably the numerical calculatio...
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In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved. Moreover, we give a set of invertible elements in split quaternion algebras and in split octonion algebras.
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Conway and Smith’s book is a wonderful introduction to the normed division algebras: the real numbers (R), the complex numbers (C), the quaternions (H) and the octonions (O). The first two are well-known to every mathematician. In constrast, the quaternions and especially the octonions are sadly neglected, so the authors rightly concentrate on these. They develop these number systems from scrat...
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Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for today's revival on interest to nonassociativity. Our reflections keep wandering back to the Brahmagupta-Fibonacci Two-Square Identity and then via the Euler Four-Square Identity up to the...
متن کاملOn quaternions and octonions: their geometry, arithmetic, and symmetry, A K
Conway and Smith’s book is a wonderful introduction to the normed division algebras: the real numbers (R), the complex numbers (C), the quaternions (H), and the octonions (O). The first two are well-known to every mathematician. In contrast, the quaternions and especially the octonions are sadly neglected, so the authors rightly concentrate on these. They develop these number systems from scrat...
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ژورنال
عنوان ژورنال: Advances in Applied Clifford Algebras
سال: 2020
ISSN: 0188-7009,1661-4909
DOI: 10.1007/s00006-020-1048-y