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  2. Collineation - Wikipedia

    en.wikipedia.org/wiki/Collineation

    In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a

  3. Collinearity - Wikipedia

    en.wikipedia.org/wiki/Collinearity

    A mapping of a geometry to itself which sends lines to lines is called a collineation; it preserves the collinearity property. The linear maps (or linear functions) of vector spaces , viewed as geometric maps, map lines to lines; that is, they map collinear point sets to collinear point sets and so, are collineations.

  4. Projective plane - Wikipedia

    en.wikipedia.org/wiki/Projective_plane

    If α is an automorphism of K, then the collineation given by (x 0, x 1, x 2) → (x 0 α, x 1 α, x 2 α) is an automorphic collineation. The fundamental theorem of projective geometry says that all the collineations of PG(2, K) are compositions of homographies and automorphic collineations. Automorphic collineations are planar collineations.

  5. Homography - Wikipedia

    en.wikipedia.org/wiki/Homography

    A central collineation (traditionally these were called perspectivities, [8] but this term may be confusing, having another meaning; see Perspectivity) is a bijection α from P to P, such that there exists a hyperplane H (called the axis of α), which is fixed pointwise by α (that is, α(X) = X for all points X in H) and a point O (called the ...

  6. Collinearity equation - Wikipedia

    en.wikipedia.org/wiki/Collinearity_equation

    Let x, y, and z refer to a coordinate system with the x- and y-axis in the sensor plane. Denote the coordinates of the point P on the object by ,,, the coordinates of the image point of P on the sensor plane by x and y and the coordinates of the projection (optical) centre by ,,.

  7. List of coordinate charts - Wikipedia

    en.wikipedia.org/wiki/List_of_coordinate_charts

    Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .

  8. AGNC Investment Wasn't a Buy in 2024, and It Won't Be a Buy ...

    www.aol.com/agnc-investment-wasnt-buy-2024...

    AGNC data by YCharts. The chart highlights two vastly different outcomes. On a stock price-only basis, AGNC Investment's price is down about 50% from its IPO. Total return, which assumes dividend ...

  9. Fano plane - Wikipedia

    en.wikipedia.org/wiki/Fano_plane

    By the Fundamental theorem of projective geometry, the full collineation group (or automorphism group, or symmetry group) is the projective linear group PGL(3, 2), [a] Hirschfeld 1979, p. 131 [3] This is a well-known group of order 168 = 2 3 ·3·7, the next non-abelian simple group after A 5 of order 60 (ordered by size).

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