  We prove that the matrix of capacitance in electrostatics is a
positive-singular matrix with a non-degenerate null eigenvalue. We explore the
physical implications of this fact, and study the physical meaning of the
eigenvalue problem for such a matrix. Many properties are easily visualized by
constructing a "potential space" isomorphic to the euclidean space. The problem
of minimizing the internal energy of a system of conductors under constraints
is considered, and an equivalent capacitance for an arbitrary number of
conductors is obtained. Moreover, some properties of systems of conductors in
successive embedding are examined. Finally, we discuss some issues concerning
the gauge invariance of the formulation.
