 Every matrix \(\cM\) can be turned into a reduced matrix by identifying the elements related by its Leibniz congruence. This matrix is called the reduction of \(\cM\) and is usually denoted by \(\cM^*\). A matrix and its reduction are models of the same logic systems, and since reduced matrices have no redundant elements, the classes of reduced matrices that are matrix semantics for logic systems are usually taken as the classes of matrices that deserve study; they are better suited to encoding in algebraic-like terms the properties of the logics that have them as their matrix semantics.