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) |

(3) |

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) |

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, p. 1106, 1979.

Le Lionnais, F. *Les nombres remarquables.* Paris: Hermann, p. 38, 1983.

© 1996-9

1999-05-26