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Norm (mathematics): Difference between revisions
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(Created page with "== Definition and Introduction == In mathematics, a '''norm''' is a function that assigns a strictly positive length or size to each vector in a vector space, save for the zero vector, which is assigned a length of zero. Norms are fundamental in various branches of mathematics, including linear algebra, functional analysis, and geometry. They provide a means to quantify the size of elements in a vector space and are essential in defining concepts such as d...") |
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The \(L^p\) norms are a family of norms that generalize the \(L^1\), \(L^2\), and \(L^\infty\) norms. They are extensively used in [[functional analysis]] and [[probability theory]]. | The \(L^p\) norms are a family of norms that generalize the \(L^1\), \(L^2\), and \(L^\infty\) norms. They are extensively used in [[functional analysis]] and [[probability theory]]. | ||
[[Image:Detail-104891.jpg|thumb|center|Illustration of vectors in a 3D space with various norms applied.]] | [[Image:Detail-104891.jpg|thumb|center|Illustration of vectors in a 3D space with various norms applied.|class=only_on_mobile]] | ||
[[Image:Detail-104892.jpg|thumb|center|Illustration of vectors in a 3D space with various norms applied.|class=only_on_desktop]] | |||
== Norms in Infinite-Dimensional Spaces == | == Norms in Infinite-Dimensional Spaces == | ||