  In this article, we give a geometric description for any invertible operator
on a finite dimensional inner--product space. With the aid of such a
description, we are able to decompose any given conformal transformation as a
product of planar rotations, a planar rotation or reflection and a scalar
transformation. Also, we are able to conclude that an orthogonal transformation
is a product of planar rotations and a planar rotation or a reflection.
