What is the Metric Tensor and How is it Used in Tensors?

[Mazulu]

I've been studying vectors, vector algebra and basis vectors from the Bernard Schutz book I bought. Last night, I had home made pizza for dinner, and left overs for breakfast; so you ask, what does this have to do with tensor calculus? Well this morning I was looking at an equation in the book,
\Lambda^{\overline{β}}_\alpha=\Lambda^\bar{\beta}_{α} (v).

But there was an extra prime in the equation that didn't make sense. That is, until I noticed that it wasn't a prime at all. It was a tiny peace of charred crust that had broken off from the pizza and landed right on the equation.

 

[Fredrik]

Yeah, pizzas are making it much more difficult to learn tensors.

 

[Mazulu]

I happen to write with a pen which is contrary to what my kindergarten teacher told me about 37 years ago. She said that math is done with a pencil so you can erase if you make a mistake. I don't remember her name, but I do know that she didn't know tensors. Erasers are a significant source of primes, hats, bars and other tiny little marks that can mess with our tensors.