Recent content by jeo23

Thanks, you've both given me a lot to think about, and I really appreciate it. Fredrik, I'm going to follow your links and see if my confusion disappears. Of course, you're right that the definition of a basis has nothing to do with how a vector looks like. I still have a question, and if I...

It's looks like you are doing the math correctly. However, I'm confused as to why you are confused. I don't see any vector that points downward.

Thanks very much for the replies. I'm going to follow up with a question which may be totally wrong, but I'm trying to get some intuition. Is there a function or set of functions to which \partiali is applied to get the standard basis { [1 0], [0 1] }? I'll explain my motivation, and...

I just would like to add that the arguments don't have to be all vectors (contravariant). They can be dual vectors (covariant) as well. As to your last question, you can have a rank (0,1) tensor that takes a single vector as input. Similarly, you can have a rank (1,0) tensor that takes a...

Well, a tensor is a multi-linear functional on vector and dual spaces, and it can take multiple arguments so I suppose in that sense it can be tought of as a multi-variable function as long as one realizes that each of the "variables" are vectors or dual vectors.

I have decided to attempt to pick up some differential geometry on my own, and I am trying to get some traction on the subject which I do by trying to reduce it to familiar and simple cases. This is a trivial case, I know, but it will go a long way in advancing my understanding. Suppose the...