[R] Geometrical Interpretation of Eigen value and Eigen vector

Simon Wood s.wood at bath.ac.uk
Thu Aug 10 14:59:48 CEST 2006

You can decompose a symmetric matrix A as 
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]]
> ______________________________________________
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> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283

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