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Thread Subject:
Eigenvector of 2*2 symmetric and equal diagoal elements

Subject: Eigenvector of 2*2 symmetric and equal diagoal elements

From: David

Date: 26 May, 2012 15:46:31

Message: 1 of 6

Hi,

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.

a = [0.8 0.4;0.4 0.8];
[d v] = eigs(a)

d =

    0.7071 -0.7071
    0.7071 0.7071


v =

    1.2000 0
         0 0.4000

The eigenvector is always the same....

Thanks in advance

Subject: Eigenvector of 2*2 symmetric and equal diagoal elements

From: Matt J

Date: 26 May, 2012 16:45:13

Message: 2 of 6

"David " <munnavinnu@gmail.com> wrote in message <jpqtsm$k2n$1@newscl01ah.mathworks.com>...
> Hi,
>
> 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.
==============

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.

Subject: Eigenvector of 2*2 symmetric and equal diagoal elements

From: David

Date: 26 May, 2012 16:54:08

Message: 3 of 6

"Matt J" wrote in message <jpr1ap$3jd$1@newscl01ah.mathworks.com>...
> "David " <munnavinnu@gmail.com> wrote in message <jpqtsm$k2n$1@newscl01ah.mathworks.com>...
> > Hi,
> >
> > 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.
> ==============
>
> 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.


Thanks a lot.... :-)

Subject: Eigenvector of 2*2 symmetric and equal diagoal elements

From: Greg Heath

Date: 27 May, 2012 14:32:05

Message: 4 of 6

On May 26, 11:46

Subject: Eigenvector of 2*2 symmetric and equal diagoal elements

From: Roger Stafford

Date: 27 May, 2012 16:54:06

Message: 5 of 6

Greg Heath <g.heath@verizon.net> wrote in message <a1379cb6-4e52-4f56-8e1d-94f0e2e2e3f1@l16g2000yqe.googlegroups.com>...
> Equal eigenvalues in 2-D 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.
- - - - - - - - - - - -
  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.)

  (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.)

Roger Stafford

Subject: Eigenvector of 2*2 symmetric and equal diagoal elements

From: Matt

Date: 27 May, 2012 20:12:51

Message: 6 of 6

On Sunday, May 27, 2012 12:54:06 PM UTC-4, Roger Stafford wrote:

> (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.)
>
> Roger Stafford


Could be a general google groups problem.

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