[R] Matrix eigenvectors in R and MatLab

[Spencer Graves]

Excellent analysis, Thomas.  An alternative to looking at EISPACK 
documentation is to do the following computations:

	(1) Values %*% diag(vectors) %*% solve(Values)

	(2) solve(Values) %*% diag(vectors) %*% Values

One of these two should return the original matrix; the other will 
likely be very different.  If so, the mystery is solved.  If (1) returns
PA9900, then

	PA9900 %*% Values = Values %*% diag(vectors)

Else

	Values %*% PA9900 = diag(vectors) %*% Values

Best Wishes,
Spencer Graves

Thomas W Blackwell wrote:
> Mikael  -
> 
> The matrix PA9900 is not a symmetric matrix.  Eigen() will
> automatically detect this.  help("eigen") says explicitly:
> 
> "For `eigen( , symmetric = FALSE)' the choice of length of
> the eigenvectors is not defined by LINPACK.  In all other
> cases the vectors are normalized to unit length."
> 
> In the example you give, the eigenvectors from R are clearly
> NOT normalized to unit length, while those from Matlab are.
> Even after normalizing them, the R eigenvectors will differ
> by order and sign from the Matlab ones.  (Compare R column 3
> with Matlab column 2.)  Have to look at the EISPACK source
> documentation to see whether it's returning right eigenvectors
> or left eigenvectors for an asymmetric matix.
> 
> -  tom blackwell  -  u michigan medical school  -  ann arbor  -
> 
> On Thu, 3 Apr 2003, Mikael Niva wrote:
> 
> 
>>Dear R-listers
>>
>>Is there anyone who knows why I get different eigenvectors when I run
>>MatLab and R? I run both programs in Windows Me. Can I make R to produce
>>the same vectors as MatLab?
>>
>>#R Matrix
>>PA9900<-c(11/24 ,10/53 ,0/1 ,0/1 ,29/43 ,1/24 ,27/53 ,0/1 ,0/1 ,13/43
>>,14/24 ,178/53 ,146/244 ,17/23 ,15/43 ,2/24 ,4/53 ,0/1 ,2/23 ,2/43 ,4/24
>>,58/53 ,26/244 ,0/1 ,5/43)
>>
>>#R-syntax
>>PA9900<-matrix(PA9900,nrow=5,byrow=T)
>>eigen(PA9900)
>>
>>#R-output
>>$values
>>[1]  1.2352970  0.3901522 -0.2562860  0.2259411  0.1742592
>>
>>$vectors
>>            [,1]        [,2]        [,3]      [,4]       [,5]
>>[1,] -0.67795430 -1.70686496 -0.52613955 -8.675109 -0.8413826
>>[2,] -0.32621100  0.54611272 -0.21526356 -2.726193 -0.2876643
>>[3,] -2.83313878 -2.88801964  0.87388189 45.427935  4.5069361
>>[4,] -0.09857565 -0.33015962  0.09136359 -5.426254 -0.8201206
>>[5,] -0.68977432  0.01977374  0.61772506  3.751978  0.4348802
>>
>>%Matlab Matrix
>>PA9900 =[11/24 10/53 0/1 0/1 29/43 ;1/24 27/53 0/1 0/1 13/43 ;14/24
>>178/53 146/244 17/23 15/43 ;2/24 4/53 0/1 2/23 2/43 ;4/24 58/53 26/244
>>0/1 5/43]
>>
>>%MatLab-syntax
>>[wmat,dmat]=eig(mat)
>>
>>%MatLab-output
>>wmat =
>>   -0.2250    0.4330   -0.4998   -0.1795   -0.1854
>>   -0.1083    0.1771    0.1599   -0.0614   -0.0583
>>   -0.9403   -0.7191   -0.8457    0.9617    0.9708
>>   -0.0327   -0.0752   -0.0967   -0.1750   -0.1160
>>   -0.2289   -0.5083    0.0058    0.0928    0.0802
>>
>>dmat =
>>    1.2353         0         0         0         0
>>         0   -0.2563         0         0         0
>>         0         0    0.3902         0         0
>>         0         0         0    0.1743         0
>>         0         0         0         0    0.2259
>>
>>Yours sincerely, Mikael Niva
>>
>>********************************************
>>Mikael Niva
>>Avd. f?r V?xtekologi, Dept. of Plant Ecology
>>EvolutionsBiologiskt Centrum, Uppsala Universitet
>>Villav?gen 14
>>752 36 UPPSALA
>>E-post Mikael.Niva at EBC.UU.SE
>>Tel. +46 (0)18 471 28 65
>>Fax +46 (0)18 55 34 19
> 
> 
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