# Category:Hilbert Spaces

This category contains results about Hilbert Spaces.

Definitions specific to this category can be found in Definitions/Hilbert Spaces.

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

Let $d: V \times V \to \R_{\ge 0}$ be the metric induced by the inner product norm $\left\Vert{\cdot}\right\Vert_V$.

If $\left({V, d}\right)$ is a complete metric space, $V$ is said to be a **Hilbert space**.

## Subcategories

This category has only the following subcategory.

### L

## Pages in category "Hilbert Spaces"

The following 39 pages are in this category, out of 39 total.

### C

- Cauchy-Bunyakovsky-Schwarz Inequality/Inner Product Spaces
- Cauchy-Bunyakovsky-Schwarz Inequality/Inner Product Spaces/Proof 1
- Cauchy-Bunyakovsky-Schwarz Inequality/Inner Product Spaces/Proof 2
- Characterization of Bases (Hilbert Spaces)
- Characterization of Invariant Subspaces
- Characterization of Reducing Subspaces
- Classification of Bounded Sesquilinear Forms
- Closed Linear Subspaces Closed under Setwise Addition
- Completion Theorem (Inner Product Space)