The Hypercomplex number reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

# Hypercomplex number

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In mathematics, hypercomplex numbers are extensions of the complex numbers constructed by means of abstract algebra, 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 sedenion can be generated by the Cayley-Dickson construction. The Clifford algebras are another family of hypercomplex numbers.

 Topics in mathematics related to quantity Edit 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 numberss | Integer sequences | Mathematical constants | Infinity