Prove that if is an eigenvalue of A with geometric multiplicity d, then is an eigenvalue

Chapter 6, Problem 9

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Prove that if is an eigenvalue of A with geometric multiplicity d, then is an eigenvalue of AT with geometric multiplicity d. (Hint: Use Theorem 4.6 of Chapter 3.)

Questions & Answers

QUESTION:

Prove that if is an eigenvalue of A with geometric multiplicity d, then is an eigenvalue of AT with geometric multiplicity d. (Hint: Use Theorem 4.6 of Chapter 3.)

ANSWER:

Step 1 of 3

According to the definition, for any matrix  having eigenvalue , the geometry multiplicity of  is equal to the number of linearly independent eigenvectors of , which is same as the dimension of the null space of .

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back