Mathematical terminology

Complete set of invariants

In mathematics, a complete set of invariants for a classification problem is a collection of maps (where is the collection of objects being classified, up to some equivalence relation , and the are some sets), such that if and only if for all . In words, such that two objects are equivalent if and only if all invariants are equal. Symbolically, a complete set of invariants is a collection of maps such that is injective. As invariants are, by definition, equal on equivalent objects, equality of invariants is a necessary condition for equivalence; a complete set of invariants is a set such that equality of these is also sufficient for equivalence. In the context of a group action, this may be stated as: invariants are functions of coinvariants (equivalence classes, orbits), and a complete set of invariants characterizes the coinvariants (is a set of defining equations for the coinvariants). (Wikipedia).

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Jordan normal form | Mathematics | Invariant (mathematics) | Euler characteristic | Genus (mathematics) | Orientability | Classification theorem