TITLE: Normalizing an eigenvector to have unit length
QUESTION [6 upvotes]: I worked out a problem where one of the eigenvectors is $(1+ \sqrt{2}, 1)$. How do I normalize this vector? Should I use approximate values?

REPLY [6 votes]: There's no need to use approximate values. You have all the exact values you need to normalize the vector.
Here's the general formula for normalizing a vector: If $v$ is the non-zero vector $(a,b)$, then the normalized vector $v$ is
$$\frac{1}{\sqrt{a^2+b^2}}(a,b).$$
What do you get?