Structure of Hypercomplex Units and Exotic Numbers as Sections of Bi-Quaternions

$113.00 plus tax (Refund Policy)

Buy Article:

Abstract:

A survey of all families of hypercomplex (HC-) numbers is suggested with emphasis on exotic sets. Systematic description of variety of representations of HC-units is given, and interior structure of the units is studied. Elementary math objects constituting the structure are demonstrated to possess variously algebraic, geometric and physical properties, being eigenfuctions of HC-vector operators, ideals of idempotent matrices, dyads (Lame coefficients) linking two 2-dimensional surfaces, projectors of matrix-vectors onto given axis, and spinors. It is also shown that full set of bi-quaternion numbers comprises as special cases real, complex, quaternion numbers and as well exotic sets split-complex and dual numbers. In particular a HC-unit of double numbers is found to be represented by a Pauli-type matrix, and a simple formula for null-modulus HC-unit of dual numbers is indicated.

Document Type: Research Article

DOI: http://dx.doi.org/10.1166/asl.2010.1135

Publication date: December 1, 2010

More about this publication?
  • ADVANCED SCIENCE LETTERS is an international peer-reviewed journal with a very wide-ranging coverage, consolidates research activities in all areas of (1) Physical Sciences, (2) Biological Sciences, (3) Mathematical Sciences, (4) Engineering, (5) Computer and Information Sciences, and (6) Geosciences to publish original short communications, full research papers and timely brief (mini) reviews with authors photo and biography encompassing the basic and applied research and current developments in educational aspects of these scientific areas.
  • Editorial Board
  • Information for Authors
  • Subscribe to this Title
  • ingentaconnect is not responsible for the content or availability of external websites
Related content

Tools

Favourites

Share Content

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more