Endomorphism/Dilation/Every vector neq 0 is eigenvector/Exercise
Let be a field, and let be an endomorphism on a -vector space . Show that is a homothety if and only if every vector , , is an eigenvector of .
Let be a field, and let be an endomorphism on a -vector space . Show that is a homothety if and only if every vector , , is an eigenvector of .