A Quadratic Form is said to be positive definite if for . A Real Quadratic Form in variables is positive definite Iff its canonical form is

 (1)

 (2)

of two Real variables is positive definite if it is for any , therefore if and the Discriminant . A Binary Quadratic Form is positive definite if there exist Nonzero and such that
 (3)

(Le Lionnais 1983).

A Quadratic Form is positive definite Iff every Eigenvalue of is Positive. A Quadratic Form with a Hermitian Matrix is positive definite if all the principal minors in the top-left corner of are Positive, in other words

 (4) (5) (6)