This thesis investigates the mathematical structure of transfer functions of frequency selective linear systems with multiple inputs and multiple outputs. The analytical and algebraical properties of the transfer function reveals whether there exists an equalizing filter with certain desired system theoretical properties. Moreover in some cases they directly determine the structure of the desired equalizer. The first part of this work considers the following general problem: Given a linear system with certain system theoretical properties. Which conditions has the transfer function to satisfy such that an equalizer with the same system theoretical properties exists which can completely invert the influence of the linear system? The approach, taken in this work, allows a quite general answer for very different system properties. The second part of this thesis investigates a special class of linear systems, namely systems with a finite impulse response. Such systems are of great practical importance since they can easily be realized in practical applications. This work shows that the algebraic structure of these systems is completely determined by its so called elementary divisors and minimal indices. These values show whether a corresponding equalizer with finite impulse response exists, and they determine the algebraic structure of these equalizers. The results are applied to different problems in filter design.