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Hilbert space
Definition
| $V$ |
| $\mathcal V \in \mathrm{Hilbert}(V)$ |
| $\mathcal V \in \mathrm{PreHilbert}(V)$ |
| $v\in \mathrm{CauchySeq}(V)$ |
| $v_\infty \in \mathcal V $ |
The space $\mathcal V$ is complete: For each Cauchy sequence $(v)_{i\in\mathbb N}$, there is a limit $v_\infty\in\mathcal V$ w.r.t. the natural norm:
| $\exists v_\infty.\ \mathrm{lim}_{n\to\infty}\Vert v_n-v_\infty \Vert = 0$ |
Discussion
Reference
Wikipedia: Hilbert space
Parents
Subset of
Requirements
