# [R] Matrix eigenvectors in R and MatLab

Thomas W Blackwell tblackw at umich.edu
Sat Apr 5 01:29:47 CEST 2003

```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. för Växtekologi, Dept. of Plant Ecology
> EvolutionsBiologiskt Centrum, Uppsala Universitet
> Villavägen 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

```