State space is one of the key concepts of system theory. In general, a state space is introduced into a system description without examining its specific physical meaning. It is known, however, that if we select a suitable state space representation, it becomes easier for us to understand or to manipulate the property of a system. Thus, although it may not be meaningful to try to arrive at a physical meaning of the state space, it is important to find a way where a choice of a state space can be made in accordance with the system of interest, taking into account the theoretical meaning of that choice. In this paper, the choice of a state space is discussed in terms of the concepts that general systems theory have provided and the canonical forms of linear control theory are interpreted using the state space representation. Four realizations of a single-input and single-output discrete basic linear system are constructed, whose state spaces are derived from system properties. such as reachability, past-determinacy, one-step ergodicity and least observability. The isomorphism between the realizations and the universal state space representation indicates a systemic meaning of the state spaces. We demonstrate that the matrix representations of the realizations, incidentally, coincide with the canonical forms and give them some meaning in relation to the universal state space representation.