词汇 | cotangent-space |
释义 | BETA cotangent spacecollocation in Englishmeanings of cotangentand spaceThese words are often used together. Click on the links below to explore the meanings. cotangent noun[ C ] uk /kəʊˈtæn.dʒənt/ us /koʊˈtæn.dʒənt/ a function (= a mathematical relation) of an angle that is the reciprocal (= number) ... See more at cotangent space noun uk /speɪs/ us /speɪs/ an empty area that is available to ... See more at space Examples of cotangent spacecotangent space Typically, the cotangentspace is defined as the dual space of the tangent space at "x", although there are more direct definitions (see below). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables (i.e. the cotangentspace of configuration space). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Likewise, cotangentspace is a contravariant functor, essentially the composition of the tangent space with the dual space above. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The cotangentspace will then consist of all the possible first-order behaviors of a function near x. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The tangent space is, the dual vector space to the cotangentspace. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The tangent space and the cotangentspace at a point are both real vector spaces of the same dimension and therefore isomorphic to each other via many possible isomorphisms. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The cotangentspace at a point is the dual of the tangent space at that point, and the cotangent bundle is the collection of all cotangent spaces. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The term "microlocal" implies localisation not only with respect to location in the space, but also with respect to cotangentspace directions at a given point. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Analytic mappings induce pushforward maps on tangent spaces and pullback maps on cotangent spaces. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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