COMPLEX NUMBER AND OTHER EXTENSIONS TO THE CLIFFORD ALGEBRA WITH AN APPLICATION TO THE THEORY OF CONTINUED FRACTIONS.
Abstract
An isomorphism between vectors whose components are complex numbers and square matrices having a certain structure is established. This isomorphism is such that the sum and difference of two vectors correspond to the sum and difference of the equivalent matrices: furthemore the inverse of a vector (this is described in the text) corresponds to the inverse of its equivalent matrix. This isomorphism is first extended so as to concern vectors whose components are quaternions, and then still further generalized to deal with what are called hyper-quaternion vectors. The isomorphism is then applied to the investigation of certain matrix continued fractions: the resulting theory establishes the existence of the vector-valued ade table. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1966
- Accession Number
- AD0638624
Entities
People
- P. Wynn