thinking about the answer to your
question before
you cut and paste it into your homework assignment.
-Original Message-
From: Dirk Enzmann [mailto:[EMAIL PROTECTED]
Sent: Sat 8/12/2006 7:01 AM
To: r-help@stat.math.ethz.ch
Cc: [EMAIL PROTECTED]
Subject: Re: [R] Geometrical Interpretation
Arun,
have a look at:
http://149.170.199.144/multivar/eigen.htm
HTH,
Dirk
Arun Kumar Saha [EMAIL PROTECTED] wrote:
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
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?
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
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.
