Category:Definitions/Hilbert Spaces

This category contains definitions related to Hilbert Spaces.
Related results can be found in Category:Hilbert Spaces.

Let $V$ be an inner product space over $\Bbb F \in \set {\R, \C}$.

Let $d: V \times V \to \R_{\ge 0}$ be the metric induced by the inner product norm $\norm {\,\cdot\,}_V$.

If $\struct {V, d}$ is a complete metric space, $V$ is said to be a Hilbert space.

Subcategories

This category has only the following subcategory.