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This paper presents a unified perspective for geometric and algebraic criteria for the reachability and controllability of switched linear systems. The direct connection between the geometric and algebraic criterion is established as well as that between the subspace algorithm for controllability/reachability and other algebraic criterion. In particular, we investigate the reachability realization problem for a class of controlled switched linear discrete-time systems. Both aperiodic and periodic switching sequences are designed to solve the problem.