ivl

Dear all,

I have a simple question for you. Any help will be very appreciated.

==Assumptions===
I have a 2x2 matrix, with real entries:

|A B|
|C D|

Such matrix has unit determinant, AD-BC=1.
(For those of you in group theory: the above is a representative of SL(2,R)).

==Question===
The above matrix, due to the unit-determinant condition, has 3 independent parameters.
So, I would like to represent the 2x2 real matrix with unit determinant in a more convenient form: a form which depends on only 3 parameters.

For instance, I could try and relate the above matrix to a rotation matrix, that is, one of the independent parameters would be a rotation angle.

Any ideas on a convenient "minimal" representation?

=========

Thanks a lot!
IVL