Tensors for dummies.

[Jehanne]

I am trying to understand them; any easy explanations from you pros?

[Alex K]

I'd be happy to help, but you need to be a bit more specific, as there is a lot one can say about tensors or do with them
In what context do you need them? Which type?

[Jehanne]

I'd be happy to help, but you need to be a bit more specific, as there is a lot one can say about tensors or do with them
In what context do you need them? Which type?

I am trying to understand general relativity at a very basic level, but I want a quantitative understanding as opposed to merely a qualitative one, although, the latter certainly is helpful with respect to the former.

[Alex K]

I'd be happy to help, but you need to be a bit more specific, as there is a lot one can say about tensors or do with them
In what context do you need them? Which type?

I am trying to understand general relativity at a very basic level, but I want a quantitative understanding as opposed to merely a qualitative one, although, the latter certainly is helpful with respect to the former.

Aaaah, very good. I assume you know some calculus?

The important - and defining - thing about tensors in GR is how they change under changes of coordinates x^mu to x'^mu. It is probably best if you start by considering how vectors (i.e. 1-tensors with an upper index), let us call it v^mu, change when you go from coordinates x^mu to x'^mu(x).

The rule is relatively straightforward and involves the derivatives of x' with respect to x. You can find it anywhere, e.g. wiki.

More general upper index tensors are then exactly the same, except that each of the indices gets the same treatment.

[Jehanne]

I am trying to understand general relativity at a very basic level, but I want a quantitative understanding as opposed to merely a qualitative one, although, the latter certainly is helpful with respect to the former.

Aaaah, very good. I assume you know some calculus?

The important - and defining - thing about tensors in GR is how they change under changes of coordinates x^mu to x'^mu. It is probably best if you start by considering how vectors (i.e. 1-tensors with an upper index), let us call it v^mu, change when you go from coordinates x^mu to x'^mu(x).

The rule is relatively straightforward and involves the derivatives of x' with respect to x. You can find it anywhere, e.g. wiki.

More general upper index tensors are then exactly the same, except that each of the indices gets the same treatment.

Okay, I'll have a look and keep this thread alive with questions!  Thanks!!

[Alex K]

I'm typing on my phone right now, hence my answers are a bit compressed...