Hi,

I can't prove it, but I'd say there is an infinity of them...

http://www.math.jussieu.fr/%7Enekovar/co/q/quad.pdf << page 31, exercise 2.3.9 at the bottom of the page. And in class, we encountered several inner products, based on quadratic forms with various coefficients...

(you can find a French version of this in the same site )