| 词汇 | tangent-space |
| 释义 | BETA tangent spacecollocation in Englishmeanings of tangentand spaceThese words are often used together. Click on the links below to explore the meanings. tangent noun[ C ] uk /ˈtæn.dʒənt/ us /ˈtæn.dʒənt/ a straight line that touches but does not cut into ... See more at tangent space noun uk /speɪs/ us /speɪs/ an empty area that is available to ... See more at space Examples of tangent spacetangent space In this bifurcation the geometrical splitting of the tangentspace is preserved but the expansion in the unstable direction degenerates near a periodic orbit. One piece of useful notation concerns the natural basis for a tangentspace induced by a set of coordinates. In the geometric way of looking at things, the kinetic energy metric is a smooth assignment of an inner product to each tangentspace of the configuration space. Notice that the identification process allows one to define a tangentspace at each point of the local model, including on the singular locus. If hyperbolic currently means the existence of some splitting of the tangentspace in one expanding direction and one contracting direction, the notion of 'expansion' is not clear. Of course, in a manifold, the notion of a derivative being diagonal does not make sense, since it maps one tangentspace into a completely different one. In this description the linearly independent vectors of the tangentspace of the groups near the vicinity of the unity element (the so-called generators) play a key role. In this case, it is not unusual to call the elements of the tangentspace the "generators" of the manifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Once the set of points generates the tangentspace the tangent algebra and its pseudoscalar follow immediately. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The elements of the tangentspace are called tangent vectors at "x". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. More strictly this defines an affine tangentspace, distinct from the space of tangent vectors described by modern terminology. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The bundle of differential forms, at each point, consists of all totally antisymmetric multilinear maps on the tangentspace at that point. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. At each point in, the tangentspace to can be considered as a subspace of the tangentspace of, which is just. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A smooth path in a smooth manifold has (at every point) the tangent vector, belonging to the tangentspace (attached to this point). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Typically, the cotangent space is defined as the dual space of the tangentspace 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. 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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