Let T:V-->V be any linear map.Suppose ch(X)=(X-c_1)^m_1...(X-c_k)^m_k is the characteristic polynomial such that c_i not equal to c_j, for all i not equal to j.Put W_i =Ker(T-ci.Identity)^m_i, with 1<=i<=k..then prove that dim(W_i)=m_i.
Let T:V-->V be any linear map.Suppose ch(X)=(X-c_1)^m_1...(X-c_k)^m_k is the characteristic polynomial such that c_i not equal to c_j, for all i not equal to j.Put W_i =Ker(T-ci.Identity)^m_i, with 1<=i<=k..then prove that dim(W_i)=m_i.