Re: [R] Beginning Eigen System question.

2010-06-23 Thread Joris Meys
Which other Linear Algebra system, and which function did you use in R?
Cheers
Joris

On Thu, Jun 24, 2010 at 12:32 AM,  rkevinbur...@charter.net wrote:
 Forgive me if I missunderstand a basic Eigensystem but when I present the 
 following matrix to most any other LinearAlgebra system:

  1  3  1
  1  2  2
  1  1  3

 I get an answer like:

 //$values
 //[1]  5.00e+00  1.00e+00 -5.536207e-16

 //$vectors
 //           [,1]       [,2]       [,3]
 //[1,] 0.5773503 -0.8451543 -0.9428090
 //[2,] 0.5773503 -0.1690309  0.2357023
 //[3,] 0.5773503  0.5070926  0.2357023

 But R gives me:

 //$values
 //[1]  5.00e+00  1.00e+00 -5.536207e-16

 //$vectors
 //           [,1]       [,2]       [,3]
 //[1,] -0.5773503 -0.8451543 -0.9428090
 //[2,] -0.5773503 -0.1690309  0.2357023
 //[3,] -0.5773503  0.5070926  0.2357023

 The only difference seems to be the sign on the first eigen vector. What am I 
 missing?

 Kevin

 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.




-- 
Joris Meys
Statistical consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

tel : +32 9 264 59 87
joris.m...@ugent.be
---
Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Beginning Eigen System question.

2010-06-23 Thread Joris Meys
On Thu, Jun 24, 2010 at 12:41 AM, Joris Meys jorism...@gmail.com wrote:
 Which other Linear Algebra system, and which function did you use in R?
 Cheers
 Joris

Never mind, off course you used eigen()...
Eigenvectors are only determined up to a constant. If I'm not mistaken
(but check the help files on it), R normalizes the eigenvectors (and
so does your other Linear Algebra system). This makes the eigenvectors
 defined up to the sign.

Cheers
Joris

 On Thu, Jun 24, 2010 at 12:32 AM,  rkevinbur...@charter.net wrote:
 Forgive me if I missunderstand a basic Eigensystem but when I present the 
 following matrix to most any other LinearAlgebra system:

  1  3  1
  1  2  2
  1  1  3

 I get an answer like:

 //$values
 //[1]  5.00e+00  1.00e+00 -5.536207e-16

 //$vectors
 //           [,1]       [,2]       [,3]
 //[1,] 0.5773503 -0.8451543 -0.9428090
 //[2,] 0.5773503 -0.1690309  0.2357023
 //[3,] 0.5773503  0.5070926  0.2357023

 But R gives me:

 //$values
 //[1]  5.00e+00  1.00e+00 -5.536207e-16

 //$vectors
 //           [,1]       [,2]       [,3]
 //[1,] -0.5773503 -0.8451543 -0.9428090
 //[2,] -0.5773503 -0.1690309  0.2357023
 //[3,] -0.5773503  0.5070926  0.2357023

 The only difference seems to be the sign on the first eigen vector. What am 
 I missing?

 Kevin

 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.




 --
 Joris Meys
 Statistical consultant

 Ghent University
 Faculty of Bioscience Engineering
 Department of Applied mathematics, biometrics and process control

 tel : +32 9 264 59 87
 joris.m...@ugent.be
 ---
 Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php




-- 
Joris Meys
Statistical consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

tel : +32 9 264 59 87
joris.m...@ugent.be
---
Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Beginning Eigen System question.

2010-06-23 Thread Ravi Varadhan
Eigenvectors are unique only up to a constant factor, so any scalar multiple
of an eigenvector is also an eigenvector.  By convention, most (all)
packages normalize the eigenvectors such that their norm is 1.  Therefore,
eigenvectors are unique up to their sign, i.e. if (+x) is an eigenvector
corresponding to an eigenvalue, then (-x) is also an eigenvector for the
same eigenvalue.

Hope this helps,
Ravi.

-Original Message-
From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
Behalf Of rkevinbur...@charter.net
Sent: Wednesday, June 23, 2010 6:32 PM
To: r-help@r-project.org
Subject: [R] Beginning Eigen System question.

Forgive me if I missunderstand a basic Eigensystem but when I present the
following matrix to most any other LinearAlgebra system:

 1  3  1
 1  2  2
 1  1  3

I get an answer like:

//$values
//[1]  5.00e+00  1.00e+00 -5.536207e-16

//$vectors
//   [,1]   [,2]   [,3]
//[1,] 0.5773503 -0.8451543 -0.9428090
//[2,] 0.5773503 -0.1690309  0.2357023
//[3,] 0.5773503  0.5070926  0.2357023

But R gives me:

//$values
//[1]  5.00e+00  1.00e+00 -5.536207e-16

//$vectors
//   [,1]   [,2]   [,3]
//[1,] -0.5773503 -0.8451543 -0.9428090
//[2,] -0.5773503 -0.1690309  0.2357023
//[3,] -0.5773503  0.5070926  0.2357023

The only difference seems to be the sign on the first eigen vector. What am
I missing?

Kevin

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Beginning Eigen System question.

2010-06-23 Thread William Revelle

Kevin,

At 3:32 PM -0700 6/23/10, rkevinbur...@charter.net wrote:
Forgive me if I missunderstand a basic Eigensystem but when I 
present the following matrix to most any other LinearAlgebra system:


 1  3  1
 1  2  2
 1  1  3

I get an answer like:

//$values
//[1]  5.00e+00  1.00e+00 -5.536207e-16

//$vectors
//   [,1]   [,2]   [,3]
//[1,] 0.5773503 -0.8451543 -0.9428090
//[2,] 0.5773503 -0.1690309  0.2357023
//[3,] 0.5773503  0.5070926  0.2357023

But R gives me:

//$values
//[1]  5.00e+00  1.00e+00 -5.536207e-16

//$vectors
//   [,1]   [,2]   [,3]
//[1,] -0.5773503 -0.8451543 -0.9428090
//[2,] -0.5773503 -0.1690309  0.2357023
//[3,] -0.5773503  0.5070926  0.2357023

The only difference seems to be the sign on the first eigen vector. 
What am I missing?


The sign of the eigen vectors is arbitrary.

From ?eigen
Recall that the eigenvectors are only defined up to a constant: even 
when the length is specified they are still only defined up to a 
scalar of modulus one (the sign for real matrices).


Bill




Kevin

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.