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collineation SUBST

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projective collineation geometria

kolineacja rzutowa f

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Not that a central collineation is uniquely defined by its center, its axis, a point and its image. en.wikipedia.org

It is a bijection that maps lines to lines, and thus a collineation. en.wikipedia.org

Some authors restrict the definition of collineation to the case where it is an automorphism. en.wikipedia.org

A mapping of a geometry to itself which sends lines to lines is called a collineation, it preserves the collinearity property. en.wikipedia.org

One may also define collineation groups for axiomatically defined projective spaces, where there is no natural notion of a projective "linear" transform. en.wikipedia.org

A duality is a collineation from a projective space onto its dual space, taking points to hyperplanes (and vice versa) and preserving incidence. en.wikipedia.org

A collineation is thus an "isomorphism" between projective spaces, or an automorphism from a projective space to itself. en.wikipedia.org

Such a mapping permutes the lines of the incidence structure, and the notion of collineation persists. en.wikipedia.org

Thus, the fixed point and fixed line structure for any collineation either form a projective plane by themselves, or a degenerate plane. en.wikipedia.org

The geometric view of a central collineation is easiest to see in a projective plane. en.wikipedia.org

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