Let S be a convex polyhedral set in the state space of a linear dynamical system. ii new proof of an algebraic condition for the set S to he positively invariant is given by the dual set of S. The condition obtained in this correspondence can be examined by solving a set of standard LP-type formulas. It is also shown that the conventional algebraic conditions have redundancies in the LP-type formulas. Discrete-time systems as well as continuous-time systems are considered.