Show that similarity of matrices is an equivalence relation. That is, verify the

Chapter 4, Problem 21

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Show that similarity of matrices is an equivalence relation.  That is, verify the following.

a. Reflexivity:  Any  matrix  is similar to itself.

b. Symmetry:  For any  matrices  and , if  is similar to , then  is similar to .

c. Transitivity:  For any  matrices ,  and , if  is similar to  and  is similar to , then  is similar to .      

Questions & Answers

QUESTION:

Show that similarity of matrices is an equivalence relation.  That is, verify the following.

a. Reflexivity:  Any  matrix  is similar to itself.

b. Symmetry:  For any  matrices  and , if  is similar to , then  is similar to .

c. Transitivity:  For any  matrices ,  and , if  is similar to  and  is similar to , then  is similar to .      

ANSWER:

Step 1 of 4

It is known that, a matrix  is similar to , if there exists an invertible matrix  such that,

                                                                  .

To show that similarity of matrices is an equivalence relation.

 

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