what is generator?
does it have an definition?
what is it used to do?
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
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.
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)
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?
See post #3 in
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).
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.
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