[R] Geometrical Interpretation of Eigen value and Eigen vector

Gabor Grothendieck ggrothendieck at gmail.com
Thu Aug 10 15:18:08 CEST 2006

A matrix M can be thought of as a linear transformation which maps
input vector x to output vector y:

     y = Mx

The eigenvectors are those "directions" that this mapping preserves.
That is if x is an eigenvector then y = ax for some scalar a.  i.e.
y lies in the same one dimensional space as x.  The only difference
is that y is dilated or contracted and possibly reversed and the scale factor
defining this dilation/contraction/reversal which corresponds to a particular
eigenvector x is its eigenvalue:  i.e. y = ax (where a is a scalar,
the eigenvalue, corresponding to eigenvector x).

In matrix terms, the eigenvectors form that basis in which the
linear transformation M has a diagonal matrix and the diagonal
values are the eigenvalues.

On 8/10/06, Arun Kumar Saha <arun.kumar.saha at gmail.com> wrote:
> Dear all,
> It is not a R related problem rather than statistical/mathematical. However
> I am posting this query hoping that anyone can help me on this matter. My
> problem is to get the Geometrical Interpretation of Eigen value and Eigen
> vector of any square matrix. Can anyone give me a light on it?
> Thanks and regards,
> Arun
>        [[alternative HTML version deleted]]
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