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I look forward to reading this!

However, I am reading the first part of the first section (explaining the basis vectors of a linear space), and see this:

http://i.imgur.com/Qizuw0K.png

That makes no sense to me, shouldn't it be more like this?

http://i.imgur.com/iKpKgSa.png

Maybe I am just not familiar with the notation, though...

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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.

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