casting 2x2 matrix with unit determinant in another form
I have a simple question for you. Any help will be very appreciated.
I have a 2x2 matrix, with real entries:
Such matrix has unit determinant, AD-BC=1.
(For those of you in group theory: the above is a representative of SL(2,R)).
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!