# Math Help - Eigenvector of 3x3 matrix

1. ## 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] ?

2. ## 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.

3. ## Re: Eigenvector of 3x3 matrix

Thank you very much bartmeijer