SupposeAis an n n matrix with all real entries and suppose is a complex eigenvalue of A

Chapter 7, Problem 9

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

SupposeAis an n n matrix with all real entries and suppose is a complex eigenvalue of A, with corresponding complex eigenvector v Cn. Set S = (A I)(A I). Prove that N(S) _= {0}. (Hint: Write v = x + iy, where x, y Rn.)

Questions & Answers

QUESTION:

SupposeAis an n n matrix with all real entries and suppose is a complex eigenvalue of A, with corresponding complex eigenvector v Cn. Set S = (A I)(A I). Prove that N(S) _= {0}. (Hint: Write v = x + iy, where x, y Rn.)

ANSWER:

Step 1 of 2

Given that,

A is matrix with all real values. That means there is no complex elements. A does not contains the elements which are in the form of .

The characteristic equation is,

The Eigen values of matrix A are  and .and which are complex values. Means they are in the form of .

Therefore,

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