An eigenvalue-based characterization of positive realness of transfer functions of single-input single-output time-invariant linear systems Is derived. Based on this characterization, we propose an efficient computational procedure to determine if a given transfer function is positive real. The input for this eigenvalue-based test is any gi ren, not necessarily minimal, state-space representation of the linear system. The test only involves standard matrix computations, such as computing eigenvalues of a matrix or a matrix pencil, Results of numerical experiments are reported.