What is generator? does it have an definition?

[jomoonrain]

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

thanks

 

[tiny-tim]

Welcome to PF!

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

thanks

Hi jomoonrain! Welcome to PF!

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

 

[jomoonrain]

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.

 

[tiny-tim]

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.

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)

 

[jomoonrain]

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

 

[Phrak]

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.

 

[jomoonrain]

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?

 

[samalkhaiat]

[jomoonrain;1891977]what is generator?
does it have an definition?
what is it used to do?

thanks

See post #3 in

www.physicsforums.com/showthread.php?t=210102

regards

sam

 

[Phrak]

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?

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).

 

[jomoonrain]

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,

 

[jomoonrain]

thanks, sam