What is Eigen value and Eigen vector ?

Question

What is Eigen value and Eigen vector, what is the benefit for using this method ?

Answer 1

Noushin is 'kinda' right.
An eigenvector is a vector that 'points' in the same direction (has invariant direction cosines) under some transform. The eigenvalue is a number that describes how the magnitude of the eigenvector is scaled by the transform. And, of course, both are functions of the transform itself and -not- the underlying vector space.

Doug

Answer 2

Here are some links below with very simple examples. It's quite surprising that there is not much out there that shows step-by-step how to find eigenvalues and eigenvectors. The general idea is to find the eigenvalues first. This is easy because you simply form the characteristic polynomial and find it's roots. The roots are the eigenvalues. Finding the eigenvectors requires some extra work, i.e. you still end up having to do matrix manipulations depending on how complex your matrix is. Do you know how to find the eigenvalues and eigenvectors of a 2x2 matrix? If not, I suggest you start with this so you can get the general idea. Then you can try computing the same for 3x3 matrices. Eventually you can start thinking about general algorithms. Do all this manually (by hand) and only use software like Matlab to check answers. Beware of Matlab's rref function in early student versions.

Answer 3

Eigen value is just the magnitude of /eigen Vector.

Answer 4

yea....

theses terms appear to you when you are trying to slove a Linear algebra problum. using this method. you can youse any number of unknow variables