# Numerical Method for calculating Eigenvector?

• May 15th 2008, 01:14 PM
zeeshanzia84
Numerical Method for calculating Eigenvector?
Hi,

I have a 4x4 matrix. I want to find the eigenvector corresponding to the highest eigenvalue for this matrix.

Can somebody point me to a straightforward numerical method for doing this?

• May 15th 2008, 02:02 PM
KGene
Quote:

Originally Posted by zeeshanzia84
Hi,

I have a 4x4 matrix. I want to find the eigenvector corresponding to the highest eigenvalue for this matrix.

Can somebody point me to a straightforward numerical method for doing this?

Wow!! In general it is difficult. Could you give more details? For instance, is it a matrix over $\mathbb{R}$?
• May 15th 2008, 02:04 PM
zeeshanzia84

Yes the matrix is indeed over R.
• May 15th 2008, 02:06 PM
KGene
Quote:

Originally Posted by zeeshanzia84

Yes the matrix is indeed over R.

Could you show me the matrix?
• May 15th 2008, 02:08 PM
Moo
Hello,

There is no general method for a matrix 4x4...
You even have to prove in a first time that the matrix is diagonalisable over $\mathbb{R}$...

What is it for ?
• May 15th 2008, 02:13 PM
KGene
Perhaps the only "general" method that I know is to find the characteristic polynomial of the matrix, then find all eigenvalues by solving this degree 4 polynomial (which is possible in general). Next, spot the highest eigenvalues, and find a corresponding eigenvector.
• May 15th 2008, 02:14 PM
Moo
Quote:

Originally Posted by KGene
Perhaps the only "general" method that I know is to find the characteristic polynomial of the matrix, then find all eigenvalues by solving this degree 4 polynomial (which is possible in general). Next, spot the highest eigenvalues, and find a corresponding eigenvector.

Yeah, this always work, but how awful it is... ! :D
I thought the guy was looking for a simplified method o.O
• May 15th 2008, 05:09 PM
zeeshanzia84