Math Help - Numerical Method for calculating Eigenvector?

1. 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?

2. 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 $\mathbb{R}$?

Yes the matrix is indeed over R.

4. Originally Posted by zeeshanzia84

Yes the matrix is indeed over R.
Could you show me the matrix?

5. 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 ?

6. 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.

7. 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... !
I thought the guy was looking for a simplified method o.O

8. pi and qi represent a set of vectors. and Q is the 4x4 matrix for which I need the eigenvector corresponding to the highest eigenvalue. I need to implement this in C++.

9. If you are a specific problem you can use this.