Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor

  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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook