  This note considers Sturm oscillation theory for regular matrix
Sturm-Liouville operators on finite intervals and for matrix Jacobi operators.
The number of space oscillations of the eigenvalues of the matrix Pr\"ufer
phases at a given energy, defined by a suitable lift in the Jacobi case, is
shown to be equal to the number of eigenvalues below that energy. This results
from a positivity property of the Pr\"ufer phases, namely they cannot cross
$-1$ in the negative direction, and is also shown to be closely linked to the
positivity of the matrix Pr\"ufer phase in the energy variable. The theory is
illustrated by numerical calculations for an explicit example.
