Let be an eigenvalue of . Then a vector that satisfies is an eigenvector.
Thus if you find a vector , satisfying and a vector with , then you're done.
You think you can do that?
I have found the eigenvalues -3 and -4 but have no idea how to find the eigenvectors. Any help? thanks.
Ok ive found a bit more but am then stuck after
2x1 + x3 = -3x1
-x2 + 3x3 = -3x2
2x1 + x3 = -3x3
And am now stuck
So you understand how we found the relations:
.
A vector that satisfies these relations is an eigenvector with .
Now we may choose arbitrary. These relations give the values of y and z. We may choose x = c arbitrary because if v is an eigenvector, cv is an eigenvector as well.
Let x = c then by the above relations follows, . Thus is an eigenvector for any .
The relations only show how relate to eachother. That's why one co-ordinate x,y or z may be freely chosen.