normed vector space वाक्य
उदाहरण वाक्य
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- In a normed vector space, one can define absolute convergence as convergence of the series of norms ( \ Sigma | b _ k | ).
- The term is most commonly used for the initial topology of a topological vector space ( such as a normed vector space ) with respect to its continuous dual.
- Then is a normed vector space ( and in particular, it is a metric space . ) All metric spaces have Hausdorff completions, so let be its completion.
- :The Q might be why we should be concerned with normed vector spaces when there are nicer ones ( Euclidean spaces with infinite-dimensional versions if needed ).
- Using the bilinear map, semi norms can be constructed to define a polar topology on the vector spaces and turn them into locally convex spaces, generalizations of normed vector spaces.
- This version of the triangle inequality reduces to the one stated above in case of normed vector spaces where a metric is induced via, with being the vector pointing from point to.
- Isometries are often used in constructions where one space is closed subset of some normed vector space and that every complete metric space is isometrically isomorphic to a closed subset of some Banach space.
- When the underlying vector space X is a ( not necessarily finite-dimensional ) normed vector space, analytic questions, irrelevant in the finite-dimensional case, need to be considered.
- A proof of this theorem for separable normed vector spaces was published in 1932 by Stefan Banach, and the first proof for the general case was published in 1940 by the mathematician Leonidas Alaoglu.
- *PM : every finite dimensional normed vector space is a Banach space, id = 6633-- WP guess : every finite dimensional normed vector space is a Banach space-- Status:
- *PM : every finite dimensional normed vector space is a Banach space, id = 6633-- WP guess : every finite dimensional normed vector space is a Banach space-- Status:
- *PM : scaling of the open ball in a normed vector space, id = 7458-- WP guess : scaling of the open ball in a normed vector space-- Status:
- *PM : scaling of the open ball in a normed vector space, id = 7458-- WP guess : scaling of the open ball in a normed vector space-- Status:
- :Because of the triangle inequality and because of axiom 2, we see that | | ?| | is a norm which turns into a normed vector space and hence also into a metric space.
- In this way, conjugation defines a " norm ", making the complex numbers a normed vector space over the real numbers : the norm of a complex number " z " is
- A common method in functional analysis, when studying normed vector spaces, is to analyze the relationship of the space to its continuous dual, the vector space of all possible continuous linear forms on the original space.
- I just wondered if anyone knew a nice word meaning " of the same length " when it comes to vectors in a normed vector space .-- talk ) 15 : 49, 8 November 2009 ( UTC)
- For example, for a vector space over \ mathbb Q one could take | \ alpha | to be the " p "-adic norm, which gives rise to a different class of normed vector spaces.
- Since the unit ball of every normed vector space is a bounded, symmetric, convex set and the unit ball of every Euclidean space is an ellipsoid, the theorem may also be formulated as a statement about ellipsoid sections of convex sets.
- :From the article-" Normed vector spaces are central to the study of linear algebra and functional analysis . " They also are very useful in all kinds of applied math, from Newtonian dynamics to the Leslie matrix of population biology.
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