ELA, Volume 9, pp. 282-289, October 2002, abstract.
Non-trivial Solutions to Certain Matrix Equations
Aihua Li and Duane Randall
The existence of non-trivial solutions to matrix equations
of a very general type over the real numbers is investigated
in this paper. The Lefschetz Fixed Point Theorem guarantees
the existence of special orthogonal matrix solutions to these
equations whenever the given matrices in the defining equations
belong to the special orthogonal group. A particular matrix
equation is studied in detail. General conditions are elaborated
under which no non-trivial solutions exist for this particular
matrix equation.