Definition:Seminorm (Scalar Product Space)

Definition

Let $\struct {V, \innerprod \cdot \cdot}$ be a scalar product space.

Let $v \in V$ be a vector.

Then the seminorm of $v$ is defined as:

$\norm v :=\sqrt {\innerprod v v}$

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Pseudo-Riemannian Metrics