Encyclopedia > Hypercomplex number

  Article Content

Hypercomplex number

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.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
1904

... physicist (+ 1967) May 6 - Harry Martinson, swedish author, winner of the Nobel Prize in literature May 11 - Salvador Dalí, artist May 17 - Jean Gabin[?], ...

 
 
 
This page was created in 33.2 ms