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#1 2011-10-28 23:29:34

sheldon69
Member
Registered: 2011-10-28
Posts: 2

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

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#2 2012-10-14 07:47:46

scientia
Member
Registered: 2009-11-13
Posts: 222

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 (2012-10-14 21:10:03)

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#3 2012-10-14 08:34:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: conjugacy classes

scientia wrote:

This step doesn't look right.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#4 2012-10-14 11:01:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,529

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#5 2012-10-14 21:10:53

scientia
Member
Registered: 2009-11-13
Posts: 222

Re: conjugacy classes

Thanks for pointing out. smile

I've corrected the error in my post.

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