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) |
See also Indefinite Quadratic Form, Positive Semidefinite Quadratic Form
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 Eric W. Weisstein