R help - Apr 2009 - the puzzle of eigenvector and eigenvalue

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?

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

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
> 
> ______________________________________________
> R-help at 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.