What is generator? does it have an definition?

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Discussion Overview

The discussion revolves around the concept of "generator," exploring its definitions and applications in both electrical engineering and mathematics, particularly in analytical and quantum mechanics. Participants seek to clarify the term and its usage in various contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants inquire about the definition of a generator and its uses, particularly in electrical contexts.
  • One participant mentions encountering the term "generator" in mathematical contexts, specifically in analytical mechanics and quantum mechanics, noting the difficulty in forming a general concept.
  • Another participant explains that in mathematics, generators can refer to a set of elements that can produce a subspace through allowable operations.
  • A participant introduces the idea of infinitesimal generators and provides an example related to rotation matrices.
  • Questions arise about whether all rotation matrices can be expressed in exponential form, with references to complex numbers and their relation to rotations.
  • Participants express gratitude for the information shared, indicating varying levels of understanding and clarity on the topic.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the definition and application of "generator," particularly between its electrical and mathematical interpretations. No consensus is reached on a singular definition or understanding.

Contextual Notes

Participants reference specific mathematical contexts and examples, but there are limitations in the clarity of definitions and the assumptions underlying the discussions about generators in different fields.

Who May Find This Useful

Individuals interested in the definitions and applications of generators in electrical engineering and mathematics, particularly those studying analytical mechanics and quantum mechanics.

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

thanks
 
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Welcome to PF!

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

thanks

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:
 


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.
 
jomoonrain said:
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! :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)
 


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


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.
 


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?
 


jomoonrain said:
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).
 
  • #10


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


thanks, sam
 

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