invariant theory

Invariant theory is a branch of mathematics that studies quantities that remain unchanged under a set of transformations. These unchanging quantities are called invariants. The concept is closely related to covariant, which describes quantities that vary in a specific way with transformations to preserve certain mathematical relationships.12

Invariant theory has found applications in various fields, including geometry. For instance, Felix Klein proposed using group theory to classify different geometries, suggesting that the properties of a geometry could be understood by examining the groups of transformations that leave its essential characteristics unchanged. This idea connects invariant properties to the structure of geometric transformations.3