A property of a system of relationships that is unchanged by any change or transformation applied to the frame of reference of the system. Thus a structure may be reflected in a plane resulting in a transformation in which every point of space is associated with its corresponding point with respect to the plane. A rotation of the structure around a line or a reflection of it with respect to the centre are similarly defined. Invariance establishes a relationship between objects, phenomena and theories which are outwardly unrelated. By an invariant of some object under study, relative to certain of its transformations, is meant any quantity, numerical, vectorial, etc connected with the object that does not vary under these transformations.
Invariance is orderly repetition of pattern of which a special form is called symmetry.