On assuming that a continuous-time time-invariant linear system (CFLS) is reachable or stabilizable, a necessary and sufficient condition is presented that the discrete-time time-invariant linear system resulting from the hold equivalence approximation to the CILS is also reachable or stabilizable. The studies are based on the eigenvalues and eigenspaces of the adjointA*of the system matrixAand the kernel of the adjointB*of the input matrixBappearing in the CILS. A necessary and sufficient condition for the observability or detectability of a CILS to be preserved after discretization is also sought.