IJPAM: Volume 61, No. 2 (2010)

SIMPLIFIED SQUARE EQUATION IN
THE QUATERNION ALGEBRA

Dušan Pagon
Faculty of Natural Sciences and Mathematics
University of Maribor
Koroška Cesta 160, Maribor, SI-2000, SLOVENIA
e-mail: [email protected]


Abstract.Quaternion arithmetics is nowadays broadly used in electrodynamics, general relativity theory Trifonov [4] and for graphical programming, where it successfully replaces tensors and other similar models. The description of the solutions of linear equation was obtained already by classics, who introduced the quaternion algebra (W.R. Hamilton, J. Sylvester), but very little is still known about the structure of the solutions of higher order algebraic equations. We give a complete description of the solutions of quaternion square equation in the case when the unknown is not mixed with the coefficients, but always stands behind them (a simplified case).

Received: May 10, 2010

AMS Subject Classification: 11R52, 20G20

Key Words and Phrases: quaternion, matrix equation, complex matrix, conjugate matrix

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 2