Vector matrix representation of octonions and their geometry
نویسندگان
چکیده
منابع مشابه
Matrix Representations of Octonions and Their Applications
As is well-known, the real quaternion division algebra H is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra O can not be algebraically isomorphic to any matrix algebras over the real number field R, because O is a non-associative algebra over R. However since O is an extension of H by the Cayley-Dickson process and is also finite-dimensional, som...
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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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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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The Leech lattice, Λ24, is represented on the space of octonionic 3vectors. It is built from two octonionic representations of E8, and is reached via Λ16. It is invariant under the octonion index cycling and doubling maps. supported in part by alien invaders.
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We develop a hierarchical matrix construction algorithm using matrix–vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses OðlognÞ applications of the matrix on structured random test vectors and Oðn lognÞ extra computational cost, where n is the dimension of the unknown matrix. Numerical examples on constructing Green’s functions ...
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ژورنال
عنوان ژورنال: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
سال: 2018
ISSN: 1303-5991
DOI: 10.1501/commua1_0000000839