Defintion |
Definition |
The dimension of the associative algebra A over the field K is its dimension as a K-vector space. |
* The complex numbers form a unitary associative algebra over the real numbers, and so do the quaternions. |
* The complex numbers form a 2-dimensional unitary associative algebra over the real numbers * The quaternions form a 4-dimensional unitary associative algebra over the reals and a 2-dimensional unitary associative algebra over the complex numbers. |