modeling linear transformation matrix

[Ganesan]

Hi,

In wireless communication applications the signal processing is
denoted by matrix-vector notations. I am looking for a corresponding
model in Geometric Algebra. The basic unit in wireless communication
is a linear transformation matrix. My question is: How can one
represent a linear transformation matrix in Geometric algebra notion.
Lets say, we have a matrix vector equations y = Hx. x and y are 3*1
vectors. H is a 3*3 matrix. H is given and is of rank 3. The elements
of the vectors and the matrices belong to the complex field. How can
we model this using Geometric Algebra so that for different values of
x, we can find the corresponding values of y.

Thanks and regards,
Ganesan.

[ehitzer]

Dear Ganesan,

I recommend that you look in the textbook of D. Hestenes, New
Foundations of Classical Mechanics, Kluwer, 1999. How to work with
matrices is described in Chapter 5. The complex numbers are no
problem, the unit pseudoscalar in Cl(3,0) squares to -1 and is
central, i.e., it commutes with all other elements of the algebra and
therefore can easily take the role of i of complex numbers.

With kind regards,
Eckhard

[Ganesan]

Thank you very much.

Regards,
Rakash.

On May 10, 3:13 am, ehitzer <hit...@mech.u-fukui.ac.jp> wrote:
> Dear Ganesan,
>
> I recommend that you look in the textbook of D. Hestenes, New
> Foundations of Classical Mechanics, Kluwer, 1999. How to work with
> matrices is described in Chapter 5. The complex numbers are no
> problem, the unit pseudoscalar in Cl(3,0) squares to -1 and is
> central, i.e., it commutes with all other elements of the algebra and
> therefore can easily take the role of i of complex numbers.
>
> With kind regards,
> Eckhard
>
> On May 9, 4:05 pm, Ganesan <rakash.sivasivagane...@gmail.com> wrote:
>
> > Hi,
>
> > In wireless communication applications the signal processing is
> > denoted by matrix-vector notations. I am looking for a corresponding
> > model in Geometric Algebra. The basic unit in wireless communication

> > is alineartransformationmatrix. My question is: How can one
> > represent alineartransformationmatrix in Geometric algebra notion.