S. Georgiev: Linear systems in quaternions


Note on the linear systems in quaternions

by Svetlin Georgiev Georgiev
Sofia University, Faculty of Mathematics and Informatics,
Department of Differential Equations, Bulgaria
e-mail : sgg2000bg_at_yahoo.com
Submited to: ISAAC 2009, Section II. 2. “Analytical , Geometrical and Numerical Methods in Clifford- and Cayley-Dickson Algebras”

Abstract

In this talk we will discuss the linear system
(1) \sum_{l=1}^r \sum_{m=1}^n p_lm^s x_m q_lm^s = A_s ,
s = 1,2, … , n ,

where n, r >= 1 are given constants,
p_lm^s, q_lm^s, A_s, l=1,…, r,  m = 1, … , n, s = 1, … , n,
are given real quaternions, x_m, m = 1, … , n, are unkown real quaternions.

Here we propose an algorithm for finding a solution to the system (1). Also, we give necessary and sufficient conditions for the solvability of the system (1) and some examples.

Source: Email by S. Georgiev, 14 April 2009.

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