# What is generator? does it have an definition?

1. Sep 28, 2008

### jomoonrain

what is generator?
does it have an definition?
what is it used to do?

thanks

2. Sep 28, 2008

### tiny-tim

Welcome to PF!

Hi jomoonrain! Welcome to PF!

If you mean an electrical generator, there's a good description at http://en.wikipedia.org/wiki/Electrical_generator

3. Sep 28, 2008

### jomoonrain

Re: Welcome to PF!

hi!
well,actually my "generator" is some mathmatical object. i encountered this word in many places:analytical mechanics, and also quantum mechanics.but its contexts are a little different. (the latest time i met this thing was in quantum mechanics, in an rotation matrix )so it's hard for me to form a general concept of it.

4. Sep 29, 2008

### tiny-tim

Hi jomoonrain!

ahah!

In that case … the concept of a generator is very similar to that of a base …

You start with a set of elements, and then you use all the allowable operations, and that "generates" a subspace (or the whole space) …

you then say that that set of elements are the generators of the subspace.

For a bit more, see http://en.wikipedia.org/wiki/Generator_(mathematics)

5. Sep 29, 2008

### jomoonrain

Re: generator

ha
thanks for you information.
i have got it, even though not too much.

6. Sep 29, 2008

### Phrak

Re: generator

The generators or a group are elements of a group from which all other elements of the group can be made by taking products of the generators.

Sometimes they talk about infintesimal generators. I like to take things by expample. Without the mathematical rigor, for a rotation in a plane, this is the matrix that rotates a vector by an infintesimal angle.

7. Sep 30, 2008

### jomoonrain

Re: generator

Thank you Phrak.
You talked about the rotation matrix, and I just have a question here.
Is it true that any rotation matrices can be wrote as an exponential form? If it is, then why?

8. Oct 1, 2008

9. Oct 3, 2008

### Phrak

Re: generator

I'm not sure what you mean. Does 'exponential form' has some concise mathematical meaning, you've read of, that I am not aware?

You can represent a vector (x,y) as a complex number x+iy. Rotation corresponds to multiplication by exp(i theta).

10. Oct 3, 2008

### jomoonrain

Re: generator

well,I read this statements in Ernest S. Abers' book:quantum mechanics.
and you just answered my question, even it was not so clearly. and i'm afraid i can't express my question better,cause what i have known is so little.
thanks,

11. Oct 8, 2008

### jomoonrain

Re: generator

thanks, sam