positive definite form

This space has a positive definite form, making it a true Hilbert space.

Lagrange proved that all positive definite forms of discriminant 1 are equivalent.

Thus, to prove Fermat's theorem it is enough to find any positive definite form of discriminant 1 that represents .

This quadratic form is split into positive and negative parts, in contrast to the positive definite form on the algebra of quaternions.