  There has been significant developments in the classification of boundary
conditions of positive symmetric systems, also known as Friedrichs systems,
after the introduction of operator theoretic framework. We take a step forward
towards applying the abstract theory to the classical framework by studying
Friedrichs systems on an interval. Dealing with some difficulties related to
the smoothness of eigenvectors, here we present an explicit expression for the
dimensions of the kernels of Friedrichs operators only in terms of the values
of the coefficients at the end-points of the interval. In particular, this
allows for a characterisation of all admissible boundary conditions, i.e.~those
leading to bijective realisations.
