  Consider vector space over non-commutative division algebra. Set of
automorphisms of this vector space is group $GL$. Group $GL$ acts on the set of
bases of vector space (basis manifold) single transitive and generates active
representation. Twin representation on basis manifold is called passive
representation. There is no automorphism associated with passive
transformation. However passive transformation generates transformation of
coordinates of vector with respect to basis. If we consider homomorphism of
vector space $V$ into vector space $W$, then we can learn how passive
transformation in vector space $V$ generates transformation of coordinates of
vector in vector space $W$. Vector in vector space $W$ is called geometric
object in vector space $V$. Covariance principle states that geometric object
does not depend on the choice of basis. I considered transformation of
coordinates of vector and polylinear map.
