You can decompose a symmetric matrix A as A=UDU' where U is a matrix of eigenvectors (in its columns), and D is a diagonal matrix of eigenvalues. Since A is symmetric, U is orthogonal. So what A does to a vector x when you form Ax has a simple geometerical interpretation: 1. x is rotated into the `eigenspace' of A, by U' 2. the elements of the rotated x are rescaled by multiplication by the eigenvalues of A. 3. The reverse of the rotation from step 1 is applied to the rescaled rotated x, by U.
Any use? > 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]] > > ______________________________________________ > [email protected] 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. -- > Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK > +44 1225 386603 www.maths.bath.ac.uk/~sw283 ______________________________________________ [email protected] 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.
