collineation in the Oxford-Paravia Italian Dictionary

Translations for collineation in the English»Italian Dictionary (Go to Italian»English)

Translations for collineation in the Italian»English Dictionary (Go to English»Italian)

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collineazione
collineation

Monolingual examples (not verified by PONS Editors)

English
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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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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It is a bijection that maps lines to lines, and thus a collineation.
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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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Not that a central collineation is uniquely defined by its center, its axis, a point and its image.
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The geometric view of a central collineation is easiest to see in a projective plane.
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More precisely, the collineation group is the projective semilinear group, which is the semidirect product of homographies by automorphic collineations.
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Some authors restrict the definition of collineation to the case where it is an automorphism.
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It is obvious now that is a collineation.
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The composition of two central collineations, while still a homography, will in general not be a central collineation.
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