  Beginning with the work of Lohe [14,15] there have been a number of papers
[3,5,8,9,11] that have generalized the Kuramoto model for phase-locking to a
non-commuting situation. Here we propose and analyze another such model. We
consider a collection of symmetric matrix-valued variables that evolve in such
a way as to try to align their eigenvector frames. The phase-locked state is
one where the eigenframes all align, and thus the matrices all commute. We
analyze the stability of the phase-locked state and show that it is stable. We
also analyze a dynamic analog of the twist states arising in the standard
Kuramoto model, and show that these twist states are dynamically unstable.
