\begin{definition}[Definition:Complete Ritz Sequence]
Let $\MM$ be a normed linear space.
Let $\sequence {\phi_n}$ be a Ritz sequence in $\MM$.
Let $\MM_n$ be an $n$-dimensional linear subspace of $\MM$, spanned by the first $n$ mappings of $\sequence {\phi_n}$.
Let $\eta_n$ be of the form:
:$\eta_n = \boldsymbol \alpha \boldsymbol \phi$
where $\boldsymbol \alpha$ is an $n$-dimensional real vector.
Suppose:
:$\forall y \in \MM: \forall \epsilon > 0: \exists \map n \epsilon \in \N: \exists \eta_n \in \MM_n: \size {\eta_n - y} < \epsilon$
{{explain|which norm is it?}}
Then the sequence $\sequence{\phi_n}$ is called '''complete''' in $\MM$.
{{NamedforDef|Walther Ritz|cat = Ritz}}
\end{definition}