Definition:Non-Negative Definite Mapping

Definition
Let $\C$ be the field of complex numbers.

Let $\F$ be a subfield of $\C$.

Let $V$ be a vector space over $\F$

Let $\innerprod \cdot \cdot: V \times V \to \mathbb F$ be a mapping.

Then $\innerprod \cdot \cdot: V \times V \to \mathbb F$ is non-negative definite :


 * $\forall x \in V: \innerprod x x \in \R_{\ge 0}$

That is, the image of $\innerprod x x$ is always a non-negative real number.

Also known as

 * Nonnegative definite mapping

Also see

 * Definition:Semi-Inner Product, where this property is used in the definition of the concept.