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 <[EMAIL PROTECTED]> 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]] > > ______________________________________________ > R-help@stat.math.ethz.ch 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. > ______________________________________________ R-help@stat.math.ethz.ch 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.