# Eigenvector of 3x3 matrix

• Apr 22nd 2012, 07:46 AM
zzizi
Eigenvector of 3x3 matrix
Hi

Could someone show me how to find the eigenvector of this matrix?

[1,0,0
0,1,0
0,0,1] ?

• Apr 22nd 2012, 08:24 AM
bartmeijer
Re: Eigenvector of 3x3 matrix
Any $x \in R^3$ will do. (1,0,0), (0,1,0), (0,0,1) form a basis.

Your matrix is the identity matrix. Its characteristic polynomial is $(1-\lambda)^3$, which has three roots, each equal to 1. This is called a degenerate eigenstructure, where every linear combination of -- in this case -- three eigenvectors will have the same eigenvalue.
Hope this helps.
• Apr 22nd 2012, 10:41 AM
zzizi
Re: Eigenvector of 3x3 matrix
Thank you very much bartmeijer