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Translations for „collineation“ in the English » Polish Dictionary (Go to Polish » English)

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English
Not that a central collineation is uniquely defined by its center, its axis, a point and its image.
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It is a bijection that maps lines to lines, and thus a collineation.
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Some authors restrict the definition of collineation to the case where it is an automorphism.
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A mapping of a geometry to itself which sends lines to lines is called a collineation, it preserves the collinearity property.
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One may also define collineation groups for axiomatically defined projective spaces, where there is no natural notion of a projective "linear" transform.
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A duality is a collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence.
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A collineation is thus an "isomorphism" between projective spaces, or an automorphism from a projective space to itself.
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Such a mapping permutes the lines of the incidence structure, and the notion of collineation persists.
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Thus, the fixed point and fixed line structure for any collineation either form a projective plane by themselves, or a degenerate plane.
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The geometric view of a central collineation is easiest to see in a projective plane.
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