Quadratic Forms: Closed Form from Values on Basis?

[Bacle]

Hi, Everyone:

I have a quadratic form q, defined on Z⁴ , and I know the value of

q on each of the four basis vectors ( I know q is not linear, and there is a sort

of "correction" for non-bilinearity between basis elements , whose values --on

all pairs (a,b) of basis elements-- I do know ).

Question: Is there a way of giving a closed form for q (preferably as a matrix)

that would allow me to compute the value at any 4-ple of Z⁴?

Thanks for any Suggestions, etc.

 

[fresh_42]

The matrix of a quadratic form is given by $q(v)=v^\tau Qv$. Treat $Q$ as variables and you get all necessary equations from the value of $q$ on the basis vectors.