two group representations D1(G) and D2(G) are equivalent <=> there exists a non-singular nxn matrix M s.t. forall g in G D1(g)=M^D2(g)M

=>D1(g1)D1(g2)=M^D2(g1)D2(g2)M

Equivalence of representations can be interpreted as a change of coordinates in the description of the vector space.

D1(g) = M^D2(g)M
let e = eigenvector
=> D1(g)e =M^D2(g)Me
=> Me -> D2(g)Me