Details:
Title  Algebraic systems of matrices and Gröbner basis theory  Author(s)  Gerald Bourgeois  Type  Article in Journal  Abstract  The problem of finding all the n × n complex matrices A , B , C such that, for all real t , e tA + e tB + e tC is a scalar matrix reduces to the study of a symmetric system ( S ) in the form: A + B + C = α I n , A 2 + B 2 + C 2 = β I n , A 3 + B 3 + C 3 = γ I n where α , β , γ are given complex numbers. Except in a special case, we solve explicitly these systems, depending on the values of the parameters α , β , γ . For this purpose, we use Gröbner basis theory. A nilpotent algebra is associated to the special case. The method used for solving ( S ) leads to complete solution of the original problem. We study also similar systems over the n × n real matrices and over the skewfield of quaternions.  Keywords  Systems of matrices, Gröbner basis, Quaternions, Nilpotent semigroup  ISSN  00243795 
URL 
http://www.sciencedirect.com/science/article/pii/S0024379508005570 
Language  English  Journal  Linear Algebra and its Applications  Volume  430  Number  8–9  Pages  2157  2169  Year  2009  Edition  0  Translation 
No  Refereed 
No 
