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Metric mathematics - Examples | A Wisdom Archive on Metric mathematics - Examples | | Metric mathematics - Examples A selection of articles related to Metric mathematics - Examples | |
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More material related to Metric Mathematics can be found here:
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Metric mathematics, Metric mathematics - Definition, Metric mathematics - Equivalence of metrics, Metric mathematics - Examples, Metric mathematics - Notes, Metric mathematics - Related concepts and alternative axiom systems, Metric mathematics - Relation of norms and metrics, Distance, Metric space, Metric tensor
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ARTICLES RELATED TO Metric mathematics - Examples | | | |  Metric mathematics - Examples: Encyclopedia II - Metric mathematics - Related concepts and alternative axiom systemsSome authors use the extended real number line and allow the distance function d to attain the value ∞. Such a metric is called an extended metric. Every extended metric can be rescaled to a finite metric (using d'(x, y) = d(x, y) / (1 + d(x, y)) or d''(x, y) = min(1, d(x, y))) and the two concepts of metric space are therefore equiva ...
See also:Metric mathematics, Metric mathematics - Definition, Metric mathematics - Notes, Metric mathematics - Examples, Metric mathematics - Equivalence of metrics, Metric mathematics - Relation of norms and metrics, Metric mathematics - Related concepts and alternative axiom systems Read more here: » Metric mathematics: Encyclopedia II - Metric mathematics - Related concepts and alternative axiom systems |
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| | | | Metric mathematics - Examples: Encyclopedia II - Metric mathematics - Relation of norms and metrics Given a normed vector space (X,||.||) we can define a metric on X by
d(x,y):=||x-y||.
The metric d is called induced by ||.||.
Conversely if a metric d on a vector space X satisfies the properties
d(x,y) = d(x+a,y+a) (translation invariance)
d(αx,αy) = |α|d(x,y) (homogenity)
then we can define a ...
See also:Metric mathematics, Metric mathematics - Definition, Metric mathematics - Notes, Metric mathematics - Examples, Metric mathematics - Equivalence of metrics, Metric mathematics - Relation of norms and metrics, Metric mathematics - Related concepts and alternative axiom systems Read more here: » Metric mathematics: Encyclopedia II - Metric mathematics - Relation of norms and metrics |
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| | | | Metric mathematics - Examples: Encyclopedia II - Metric mathematics - Definition A metric on a set X is a function (called the distance function or simply distance)
d : X × X → R
(where R is the set of real numbers). For all x, y, z in X, this function is required to satisfy the following conditions:
d(x, y) ≥ 0 (non-negativity)
d(x, y) = 0 if and only if x = y (identity ...
See also:Metric mathematics, Metric mathematics - Definition, Metric mathematics - Notes, Metric mathematics - Examples, Metric mathematics - Equivalence of metrics, Metric mathematics - Relation of norms and metrics, Metric mathematics - Related concepts and alternative axiom systems Read more here: » Metric mathematics: Encyclopedia II - Metric mathematics - Definition |
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