Category:Examples of Semi-Inner Products

This category contains examples of Semi-Inner Product.

A (complex) semi-inner product is a mapping $\innerprod \cdot \cdot: V \times V \to \GF$ that satisfies the (complex) semi-inner product axioms:

$(1)$	$:$	Conjugate Symmetry	$\ds \forall x, y \in V:$	$\ds \quad \innerprod x y = \overline {\innerprod y x} $
$(2)$	$:$	Sesquilinearity	$\ds \forall x, y, z \in V, \forall a \in \GF:$	$\ds \quad \innerprod {a x + y} z = a \innerprod x z + \innerprod y z $
$(3)$	$:$	Non-Negative Definiteness	$\ds \forall x \in V:$	$\ds \quad \innerprod x x \in \R_{\ge 0} $

Pages in category "Examples of Semi-Inner Products"

The following 2 pages are in this category, out of 2 total.

\((1)\)	$:$	Conjugate Symmetry	\(\ds \forall x, y \in V:\)	\(\ds \quad \innerprod x y = \overline {\innerprod y x} \)
\((2)\)	$:$	Sesquilinearity	\(\ds \forall x, y, z \in V, \forall a \in \GF:\)	\(\ds \quad \innerprod {a x + y} z = a \innerprod x z + \innerprod y z \)
\((3)\)	$:$	Non-Negative Definiteness	\(\ds \forall x \in V:\)	\(\ds \quad \innerprod x x \in \R_{\ge 0} \)