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.
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.
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
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps