# Category:Hilbert Spaces

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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 $\Bbb F \in \set {\R, \C}$.

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 the following 4 subcategories, out of 4 total.

### C

### G

### I

### L

## Pages in category "Hilbert Spaces"

The following 38 pages are in this category, out of 38 total.

### C

- Cauchy-Bunyakovsky-Schwarz Inequality/Inner Product Spaces
- 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)