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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.

scientia

Member

Registered: 2009-11-13

Posts: 224

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)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: conjugacy classes

This step doesn't look right.

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“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
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: conjugacy classes

Hi all;

This step doesn't look right.

You are correct.

Hi scientia;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

scientia

Member

Registered: 2009-11-13

Posts: 224

Re: conjugacy classes

Thanks for pointing out.

I've corrected the error in my post.