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.

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- December 11th 2009, 01:35 AMmath.djcharacteristic polynomial
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.