  We generalize entanglement detection with covariance matrices for an
arbitrary set of observables. A generalized uncertainty relation is constructed
using the covariance and commutation matrices, then a criterion is established
by performing a partial transposition on the operators. The method is highly
efficient and versatile in the sense that the set of measurement operators can
be freely chosen, do not need to be complete, and there is no constraint on the
commutation relations. The method is particularly suited for systems with
higher dimensionality since the computations do not scale with the dimension of
the Hilbert space rather they scale with the number of chosen observables which
can always be kept small. We illustrate the approach by examining the
entanglement between two spin ensembles, and show that it detects entanglement
in a basis independent way.
