A quadratic form 
is said to be positive semidefinite if it is never 
.
However, unlike a positive definite
quadratic form, there may exist a 
such that the form is zero. The quadratic
form, written in the form 
, is positive semidefinite iff
every eigenvalue of 
is nonnegative.
Positive Semidefinite Quadratic Form
See also
Indefinite Quadratic Form, Positive Definite Quadratic FormExplore with Wolfram|Alpha
References
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1106, 2000.Referenced on Wolfram|Alpha
Positive Semidefinite Quadratic FormCite this as:
Weisstein, Eric W. "Positive Semidefinite Quadratic Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PositiveSemidefiniteQuadraticForm.html