Algebraic Structures Matrix

**mrks1d** · May 18th 2008, 09:06 AM

I really need help, i need to investigate the properties of the set of matrices
a -b
b a :a,b belongs to real numbers

I need to know

transformation properties
diagonalisation
group properties
subgroups
Isomorphism

Any help would be fantastic!

thanks!

**Isomorphism** · May 18th 2008, 09:21 AM

You will have to be more specific than that to get useful answers. For the second part, I dont think you can diagonalize it(over reals) since its eigenvalues are always complex.

What transformational property do you want? What group, subgroup properties are you looking at?

**mrks1d** · May 18th 2008, 11:37 AM

I think that is why i am having the problem! That is exactly how the question is worded no extra information is given.

**Moo** · May 18th 2008, 11:44 AM

Hello,

Originally Posted by mrks1d

I think that is why i am having the problem! That is exactly how the question is worded no extra information is given.

But it's not a problem to diagonalise it over $\mathbb{C}$ o.O
The eigenvectors will remain over $\mathbb{R}$

$\chi_A(\lambda)=(a-\lambda)^2+b^2=(a-\lambda-ib)(a-\lambda+ib)$

$\lambda_1=a+ib$
$\lambda_2=a-ib$

Then find the eigenvectors. To solve for X(x,y), representing the eigenvector, just remember that if a complex number is null, it means that its real part is zero and its imaginary part is zero..

Thread: Algebraic Structures Matrix

LinkBack

Thread Tools

Display

Algebraic Structures Matrix

Similar Math Help Forum Discussions

Existence of binary operation such that two algebraic structures are isomorphic.

Problem solving algebraic structures task

About Subgroups( Algebraic Structures)

About orders of elements(Algebraic structures-subgroups)

Names of algebraic structures

Search Tags