Algebraic systems of matrices and Gröbner basis theory

@article{Bourgeois2009AlgebraicSO,
title={Algebraic systems of matrices and Gr{\"o}bner basis theory},
author={G. Bourgeois},
journal={Linear Algebra and its Applications},
year={2009},
volume={430},
pages={2157-2169}
}

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 Grobner basis theory. A nilpotent algebra… Expand