  This paper studies an optimization problem on the sum of traces of matrix
quadratic forms on $m$ orthogonal matrices, which can be considered as a
generalization of the synchronization of rotations. While the problem is
nonconvex, the paper shows that its semidefinite programming relaxation can
solve the original nonconvex problems exactly, under an additive noise model
with small noise in the order of $O(-m^{1/4})$, where $m$ is the number of
orthogonal matrices. This result can be considered as a generalization of
existing results on phase synchronization.
