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What is generator? does it have an definition?

  1. Sep 28, 2008 #1
    what is generator?
    does it have an definition?
    what is it used to do?

  2. jcsd
  3. Sep 28, 2008 #2


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    Welcome to PF!

    Hi jomoonrain! Welcome to PF! :smile:

    If you mean an electrical generator, there's a good description at http://en.wikipedia.org/wiki/Electrical_generator :smile:
  4. Sep 28, 2008 #3
    Re: Welcome to PF!

    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.
  5. Sep 29, 2008 #4


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    Hi jomoonrain! :smile:

    ahah! :biggrin:

    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. :smile:

    For a bit more, see http://en.wikipedia.org/wiki/Generator_(mathematics)
  6. Sep 29, 2008 #5
    Re: generator

    thanks for you information.
    i have got it, even though not too much.
  7. Sep 29, 2008 #6
    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.
  8. Sep 30, 2008 #7
    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?
  9. Oct 1, 2008 #8


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  10. Oct 3, 2008 #9
    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).
  11. Oct 3, 2008 #10
    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.
  12. Oct 8, 2008 #11
    Re: generator

    thanks, sam
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