# IJPAM: Volume 61, No. 2 (2010)

**SIMPLIFIED SQUARE EQUATION IN**

THE QUATERNION ALGEBRA

THE QUATERNION ALGEBRA

Faculty of Natural Sciences and Mathematics

University of Maribor

Koroška Cesta 160, Maribor, SI-2000, SLOVENIA

e-mail: dusan.pagon@uni-mb.si

**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