[R] the puzzle of eigenvector and eigenvalue

Duncan Murdoch murdoch at stats.uwo.ca
Fri Apr 24 17:35:31 CEST 2009


On 4/24/2009 10:30 AM, Abelian wrote:
> Dear all
> I am so glad the R can provide the efficient calculate about
> eigenvector and eigenvalue.
> However, i have some puzzle about the procedure of eigen.
> Fristly, what kind of procedue does the R utilize such that the eigen
> are obtained?
> For example, A=matrix(c(1,2,4,3),2,2)
> we can define the eigenvalue lamda, such as
> 
>    det | 1-lamda     4        |  =0
>          |    2        3-lamda  |
> 
> then we can obtain the lamda=5 and -1
> however, i am interesting in that how does the R to obatin lamda?
> By the way, how does the R also obtain the eigenvector?

The documentation for eigen says,

"     By default 'eigen' uses the LAPACK routines DSYEVR, DGEEV, ZHEEV
      and ZGEEV whereas 'eigen(EISPACK=TRUE)' provides an interface to
      the EISPACK routines 'RS', 'RG', 'CH' and 'CG'.   "

So you would need to consult the documentation for those functions 
(which is listed in the references) for details.

Duncan Murdoch

> 
> Basically, i must to know those definition in the R because i have to
> utilize eigenvalue and eigenvector to develope SVD (single value
> decomposition) by myself. Furthermore, i want to obtain the bi-plot
> about my data.
> Although someone suggest that i can obtain those result by R (base),
> there are exist some tough problems which is difficult to solve it. My
> data is too huge to do it. for example, the size of matrix is
> 400000*800.
> So, i think that i should follow whole steps by myself.
> 
> Finally, it is also my serious problem in the R, I have three
> estimators which work for the same data.
> Moreover, i utilize the biplot to realize those tendency. But i find
> that the the tendency of third estimator mirror the other two, the
> figures are linked below
> 
> http://hopjimmy123.pixnet.net/album/photo/108526615#pictop
> 
> i believe that the tendency should have the same way with the other
> estimator and the major problem is about the eigenvalue, i hope that
> someone can give me some idea or provide me some solution about this
> problem.
> Sincerely
> 
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