Orthonormal Set of Eigenvectors of A

Problem:

http://img46.imageshack.us/img46/5769/capture2br.jpg

Part (a): This part seems simple. I just find the eigenvectors of the matrix A, use the GS process, and then normalize to get an orthonormal set. Is this correct?

Part (b): I'm not sure how to do this part. Is "S" referring to [S]B? That is, do I use the eigenvectors of A=[S]B? I'm pretty lost here...

Part (c): Not sure how to do this without completing part b.

Any help will be appreciate and I'll click the thank you button for you! Thanks! :)

Re: Orthonormal Set of Eigenvectors of A

Quote:

Originally Posted by

**divinelogos** Problem:

http://img46.imageshack.us/img46/5769/capture2br.jpg
Part (a): This part seems simple. I just find the eigenvectors of the matrix A, use the GS process, and then normalize to get an orthonormal set. Is this correct?

Part (b): I'm not sure how to do this part. Is "S" referring to [S]B? That is, do I use the eigenvectors of A=[S]B? I'm pretty lost here...

Part (c): Not sure how to do this without completing part b.

Any help will be appreciate and I'll click the thank you button for you! Thanks! :)

I'm sorry, is this for a takehome exam?

Re: Orthonormal Set of Eigenvectors of A

Quote:

Originally Posted by

**Drexel28** I'm sorry, is this for a takehome exam?

Nope. It's a study guide for the final. I can send you the whole thing if you need to verify that. Thanks! :)

Re: Orthonormal Set of Eigenvectors of A

(a) The eigenvalues of are (double) and (simple). We have and an orthogonal basis is .

Now, and a basis is .

Hence, is an orthonormal basis of eigenvectors of .

(b)

Hope you can continue.