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?
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$\begingroup$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?
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