Let T be a linear operator on a finite-dimensional vector space V, and suppose that the distinct eigenvalues of T are λ1, λ2, . . . , λk. Prove that span({x ∈V: x is an eigenvector of T}) = Eλ1⊕Eλ2⊕· · ·⊕Eλk.

Let T be a linear operator on a finite-dimensional vector space V, and suppose that the distinct eigenvalues of T are λ1, λ2, . . . , λk. Prove that span({x ∈V: x is an eigenvector of T}) = Eλ1⊕Eλ2⊕· · ·⊕Eλk.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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