 A generalized matrix is reduced if its Tarski congruence is the identity. Every generalized matrix \(\langle \bA, \cB \rangle\) can be turned into an equivalent reduced one by identifying the elements related by its Tarski congruence. The result is the quotient generalized matrix \(\langle \bA / \bOmega^{\sim}_{\bA }(\cB), \cB/\bOmega^{\sim}_{\bA }(\cB) \rangle\), where \(\cB/\bOmega^{\sim}_{\bA }(\cB) = \{X/\bOmega^{\sim}_{\bA }(\cB): X \in \cB\}\) and for \(X \in \cB\), the set \(X/\bOmega^{\sim}_{\bA }(\cB)\) is that of the equivalence classes of the elements of \(X\).