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  \equiv \begin{Bmatrix}-x_1+x_3=0\\x_1-x_3=0\end{matrix} )
and an orthogonal basis is ^t,(0,1,0)^t\})
.
Now,  \equiv \begin{Bmatrix}x_1+x_3=0\\2x_2=0\\x_1+x_3=0\end{ma trix} )
and a basis is ^t\})
.
Hence, ^t,(0,1,0)^t,(1/\sqrt{2},0,-1/\sqrt{2})^t\})
is an orthonormal basis of eigenvectors of .
(b) ^t\equiv (1/\sqrt{2})\vec{u_1}+(1/\sqrt{2})\vec{u_3}=\ldots)
Hope you can continue.
