A community for students.
Here's the question you clicked on:
← 55 members online
 0 viewing
anonymous
 5 years ago
Let V be a finite dimensional vector space over the field of complex numbers (C), and let T be an invertible linear operator on V. Prove that if c doesn't equal 0 is an eiganvalue of T, then 1/c is an eiganvalue of T^1
anonymous
 5 years ago
Let V be a finite dimensional vector space over the field of complex numbers (C), and let T be an invertible linear operator on V. Prove that if c doesn't equal 0 is an eiganvalue of T, then 1/c is an eiganvalue of T^1

This Question is Closed

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Suppose \(x\) is the eigen vector of \(T\) corresponds to the eigne value \(c\). Then \(T(x)=cx\) Now \(x=T^{1}(T(x))=T^{1}(cx)=cT^{1}(x)\) Therefore \(T^{1}(x)=\frac{1}{c} x\).
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.