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Sat, 26 May 2012 15:46:31 +0000
Eigenvector of 2*2 symmetric and equal diagoal elements
http://www.mathworks.com/matlabcentral/newsreader/view_thread/320454#878055
David
Hi,<br>
<br>
I am trying to find the eigenvalue and eigenvector of a 2*2 matrix which is symmetric and have same diagonal elements. Even though I am changing the values of the matrix, the eigenvector remains same, only eigenvalues are changing. Why is this happening.<br>
<br>
a = [0.8 0.4;0.4 0.8];<br>
[d v] = eigs(a)<br>
<br>
d =<br>
<br>
0.7071 0.7071<br>
0.7071 0.7071<br>
<br>
<br>
v =<br>
<br>
1.2000 0<br>
0 0.4000<br>
<br>
The eigenvector is always the same....<br>
<br>
Thanks in advance

Sat, 26 May 2012 16:45:13 +0000
Re: Eigenvector of 2*2 symmetric and equal diagoal elements
http://www.mathworks.com/matlabcentral/newsreader/view_thread/320454#878060
Matt J
"David " <munnavinnu@gmail.com> wrote in message <jpqtsm$k2n$1@newscl01ah.mathworks.com>...<br>
> Hi,<br>
> <br>
> I am trying to find the eigenvalue and eigenvector of a 2*2 matrix which is symmetric and have same diagonal elements. Even though I am changing the values of the matrix, the eigenvector remains same, only eigenvalues are changing. Why is this happening.<br>
==============<br>
<br>
The sum along the rows of such a matrix will always be the same for every row. Hence [1;1] and its scalar multiples will always be an eigenvector. Similar ideas apply to the difference of the row elements.

Sat, 26 May 2012 16:54:08 +0000
Re: Eigenvector of 2*2 symmetric and equal diagoal elements
http://www.mathworks.com/matlabcentral/newsreader/view_thread/320454#878061
David
"Matt J" wrote in message <jpr1ap$3jd$1@newscl01ah.mathworks.com>...<br>
> "David " <munnavinnu@gmail.com> wrote in message <jpqtsm$k2n$1@newscl01ah.mathworks.com>...<br>
> > Hi,<br>
> > <br>
> > I am trying to find the eigenvalue and eigenvector of a 2*2 matrix which is symmetric and have same diagonal elements. Even though I am changing the values of the matrix, the eigenvector remains same, only eigenvalues are changing. Why is this happening.<br>
> ==============<br>
> <br>
> The sum along the rows of such a matrix will always be the same for every row. Hence [1;1] and its scalar multiples will always be an eigenvector. Similar ideas apply to the difference of the row elements.<br>
<br>
<br>
Thanks a lot.... :)

Sun, 27 May 2012 14:32:05 +0000
Re: Eigenvector of 2*2 symmetric and equal diagoal elements
http://www.mathworks.com/matlabcentral/newsreader/view_thread/320454#878121
Greg Heath
On May 26, 11:46

Sun, 27 May 2012 16:54:06 +0000
Re: Eigenvector of 2*2 symmetric and equal diagoal elements
http://www.mathworks.com/matlabcentral/newsreader/view_thread/320454#878129
Roger Stafford
Greg Heath <g.heath@verizon.net> wrote in message <a1379cb64e524f568e1d94f0e2e2e3f1@l16g2000yqe.googlegroups.com>...<br>
> Equal eigenvalues in 2D implies the data is circularly symmetric. Any two perpendicular unit vectors are valid solutions. Your particular answer is just a choice arbitrarily made in the coding. Any rotation of axes will result in other valid solutions.<br>
           <br>
Greg, David is not saying the eigenvalues are equal. He is saying with changing matrices of the type he is referring to, their two eigenvectors remain unchanged. There is nothing arbitrary about those eigenvectors he obtained (except for their sign of course.)<br>
<br>
(Reminder: Your replies are still not coming through fully in the Mathworks Newsreader, Greg. I had to access Google Groups to see what you were saying here.)<br>
<br>
Roger Stafford

Sun, 27 May 2012 20:12:51 +0000
Re: Eigenvector of 2*2 symmetric and equal diagoal elements
http://www.mathworks.com/matlabcentral/newsreader/view_thread/320454#878135
Matt
On Sunday, May 27, 2012 12:54:06 PM UTC4, Roger Stafford wrote:<br>
<br>
> (Reminder: Your replies are still not coming through fully in the Mathworks Newsreader, Greg. I had to access Google Groups to see what you were saying here.)<br>
> <br>
> Roger Stafford<br>
<br>
<br>
Could be a general google groups problem.