Let T:V to V be linear with finite dimV=n, if f(x)=(-1)^n (x-λ_1)^α_1...(x-λ_r)^α_r Let W be a nonzero invariant T subspace of V. Prove that there exists v in W and such that v is an eigenvector of T, with v different of 0.

icon
Related questions
Question

Let T:V to V be linear with finite dimV=n, if f(x)=(-1)^n (x-λ_1)^α_1...(x-λ_r)^α_r
Let W be a nonzero invariant T subspace of V. Prove that there exists v in W and such that v is an eigenvector of T, with v different of 0.   

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Similar questions