The following claim is in the text of the book I am reading on Differential Geometry (Curves and Surfaces, 2nd Edition, by Montiel and Ros):
It is a matter of elementary linear algebra that the sign of a quadratic form on a real vector plane is mainly controlled by its determinant.
What does this mean, precisely? How to prove this?
The context is the definition of elliptic and hyperbolic points on a surface.
Thanks in advance.