Back Teoria d'invariants Catalan Teorie invariantů Czech Invarianta teorio Esperanto نظریه ناوردا Persian Théorie des invariants French 불변량 이론 Korean Invariantentheorie Dutch Teoria dos invariantes Portuguese Теория инвариантов Russian Теорія інваріантів Ukrainian
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations from a given linear group. For example, if we consider the action of the special linear group SLn on the space of n by n matrices by left multiplication, then the determinant is an invariant of this action because the determinant of A X equals the determinant of X, when A is in SLn.