Linear Algebra

A-12We call each part of a partition an equivalence class (or informally, ‘part’).We somtimes pick a single element of each equivalence class to be the classrepresentative.⋆⋆⋆⋆. . .Usually when we pick representatives we have some natural scheme in mind. Inthat case we call them the canonical representatives.An example is the simplest form of a fraction. We’ve defined 3/5 and 9/15to be equivalent fractions. In everyday work we often use the ‘simplest form’ or‘reduced form’ fraction as the class representatives.⋆ 1/1⋆ 1/2⋆ 0/1⋆ 4/3. . .