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Positive Semidefinite Quadratic Form

A Quadratic Form $Q({\bf x})$ is positive semidefinite if it is never $<0$, but is 0 for some ${\bf x}\not={\bf0}$. The Quadratic Form, written in the form $({\bf x}, {\hbox{\sf A}}{\bf x})$, is positive semidefinite Iff every Eigenvalue of ${\hbox{\sf A}}$ is Nonnegative.

See also Indefinite Quadratic Form, Positive Definite Quadratic Form


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

© 1996-9 Eric W. Weisstein