Linear Functional - Visualizing Linear Functionals

Visualizing Linear Functionals

In finite dimensions, a linear functional can be visualized in terms of its level sets. In three dimensions, the level sets of a linear functional are a family of mutually parallel planes; in higher dimensions, they are parallel hyperplanes. This method of visualizing linear functionals is sometimes introduced in general relativity texts, such as Gravitation by Misner, Thorne & Wheeler (1973).

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