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#1 2011-10-29 22:29:34

sheldon69
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conjugacy classes

Hi, another question from my textbook I can't seem to get.

Q: Let G be the group of matrices of the form

where
and
. Determine the conjugacy classes in G, and sketch them in the (x,y)-plane.

Thanks for any help. smile

#2 2012-10-15 06:47:46

scientia
Full Member

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Re: conjugacy classes

The inverse of the matrix
is
. Let's calculate the conjugate of the matrix
by the matrix
:







Hence the conjugacy class containing
is
.

Last edited by scientia (2012-10-15 20:10:03)

#3 2012-10-15 07:34:07

anonimnystefy
Real Member

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Re: conjugacy classes

scientia wrote:



This step doesn't look right.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#4 2012-10-15 10:01:56

bobbym
Administrator

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Re: conjugacy classes

Hi all;

anonimnystefy wrote:

This step doesn't look right.

You are correct.

Hi scientia;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2012-10-15 20:10:53

scientia
Full Member

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Re: conjugacy classes

Thanks for pointing out. smile

I've corrected the error in my post.

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