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Hypercomplex number Redirected from Hypercomplex numbers
Hypercomplex 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.
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