You're right, it's a typo, the sum was on the wrong side. I fixed the equation. Thanks for catching it. Please let me know if you find any other issues. I wrote

You're right, it's a typo, the sum was on the wrong side. I fixed the equation. Thanks for catching it. Please let me know if you find any other issues. I wrote the original notes a while ago and I had to do some adjustments to make the LaTeX source work with MathJax so there might be other typos. BTW, |u> = u_i |e_i> would be the correct equation in Einstein notation where the u_i |e_i> would be a contraction in which the summation along repeated indices is implicit. When you're dealing with a lot of tensor multiplication this notation is very useful because of its clarity and compactness.