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Hypercomplex_number (including recent related patents.)
Hypercomplex numberHypercomplex numbers are extensions of the complex numbers, such as quaternions, octonions and sedenions. Whereas complex numbers can be viewed as points in a plane, hypercomplex numbers can be viewed as points in some higher-dimensional Euclidean space (4 dimensions for the quaternions, 8 for the octonions, 16 for the sedenions). More precisely, they form finite-dimensional algebras over the real numbers. But none of these extensions forms a field, essentially because the field of complex numbers is algebraically closed - see fundamental theorem of algebra. The quaternions, octonions and sedenions are generated by the Cayley-Dickson construction. The Clifford algebras are another family of hypercomplex numbers. Topics in mathematics related to quantity Numbers | Natural numbers | Integers | Rational numbers | Real numbers | Complex numbers | Hypercomplex numbers | Quaternions | Octonions | Sedenions | Hyperreal numbers | Surreal numbers | Ordinal numbers | Cardinal numbers | p-adic numbers | Integer sequences |Mathematical constants | InfinityThis article is adapted from from Wikipedia All Wikipedia article text is available under the terms of the GNU Free Documentation License Harmonic Analysis in Hypercomplex Systems (Mathematics and Its Applications (Kluwer Academic Publishers), V. 434.) by Iu. M. Berezanskii Hypercomplex Numbers by Springer Verlag Hypercomplex Numbers: An Elementary Introduction to Algebras by A.S. Solodovnikov Recent Hypercomplex_number related patents From USPTO: |