Definition:Graph Parametrization

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Definition

Let $U \subseteq \R^n$ be an open subset of $n$-dimensional Euclidean space.

Let $f : U \to \R^k$ be a real function.

Let $\map \Gamma f$ be the graph of $f$.

Let $\gamma_f : U \to \R^n \times \R^k$ be a mapping such that:

$\map {\gamma_f} u = \tuple {u, \map f u}$


Then $\gamma_f$ is called the graph parametrization (of $\map \Gamma f$).


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