Gramschmidt and scalar product

[Tonig00]

Hello
The explanation of this function says:
" Given a basis of a vector subspace, and a function that defines a scalar product, returns an orthonormal basis for that function".

I do not know how to it, I will put an example:
Scalar product defined by: <(x1,x2),(y1,y2)> = x1y1-x1y2-x2y1+2x2y2
Given a basis such as: B={(1,2), (3,4)}

How can I use the function to get an orthonormal basis?
If I put
gramschmidt([[1 2][3 4]],(a,b,c,d)->(a*b-a*d-b*c+2*b*d))

Gives me an error "Bad Argument Value"

Is there a way to do this?

Thanks in advance

Toni

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