How Many Quadratic Forms Exist on Fp^n for an Odd Prime p?

[alvielwj]

For an odd prime number p let Fp be the field with p elements, ie. the integers {0...,p-1} with addition and multiplication defined modulo p. How many quadratic forms are there on the vector space Fp^n

I don even know how to start this question

 

[alvielwj]

are there infinite many quadratic forms on the vector space R^n ?

 

[adriank]

If F is any field with characteristic not 2, on Fⁿ the quadratic forms are equivalent to the symmetric bilinear forms (essentially the symmetric n × n matrices over F).