| 词汇 | collineation |
| 释义 | BETA Examples of collineationcollineation isn’t in the Cambridge Dictionary yet. You can help! Such a mapping permutes the lines of the incidence structure, and the notion of collineation persists. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Some authors restrict the definition of collineation to the case where it is an automorphism. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A duality is a collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Every affine vector field is a curvature collineation. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. One may also define collineation groups for axiomatically defined projective spaces, where there is no natural notion of a projective "linear" transform. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Thus, the fixed point and fixed line structure for any collineation either form a projective plane by themselves, or a degenerate plane. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A mapping of a geometry to itself which sends lines to lines is called a collineation, it preserves the collinearity property. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Synonyms include projectivity, projective transformation, and projective collineation. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The composition of two central collineations, while still a homography, will in general not be a central collineation. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Not that a central collineation is uniquely defined by its center, its axis, a point and its image. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. More precisely, the collineation group is the projective semilinear group, which is the semidirect product of homographies by automorphic collineations. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A collineation is an invertible (or more generally one-to-one) map which sends collinear points to collinear points. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Indeed, cross-ratio is invariant under any collineation, and the stable absolute enables the metric comparison, which will be equality. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is obvious now that is a collineation. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A collineation is thus an "isomorphism" between projective spaces, or an automorphism from a projective space to itself. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is a bijection that maps lines to lines, and thus a collineation. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The geometric view of a central collineation is easiest to see in a projective plane. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A permutation of the seven points that carries collinear points (points on the same line) to collinear points is called a "collineation" or "symmetry" of the plane. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. |
反思网英语在线翻译词典收录了377474条英语词汇在线翻译词条，基本涵盖了全部常用英语词汇的中英文双语翻译及用法，是英语学习的有利工具。