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  2. Projective geometry - Wikipedia

    en.wikipedia.org/wiki/Projective_geometry

    In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (projective space) and a selective set of basic geometric concepts.

  3. Projective line - Wikipedia

    en.wikipedia.org/wiki/Projective_line

    In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a point at infinity.The statement and the proof of many theorems of geometry are simplified by the resultant elimination of special cases; for example, two distinct projective lines in a projective plane meet in exactly one point (there is no "parallel" case).

  4. Projection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Projection_(mathematics)

    In mathematics, a projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure). In this case, idempotent means that projecting twice is the same as projecting once. The restriction to a subspace of a projection is also called a projection, even if the idempotence property is lost. An everyday ...

  5. Vector projection - Wikipedia

    en.wikipedia.org/wiki/Vector_projection

    The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b ⁡ a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .

  6. Projection (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Projection_(linear_algebra)

    A square matrix is called a projection matrix if it is equal to its square, i.e. if =. [2]: p. 38 A square matrix is called an orthogonal projection matrix if = = for a real matrix, and respectively = = for a complex matrix, where denotes the transpose of and denotes the adjoint or Hermitian transpose of .

  7. Distance from a point to a line - Wikipedia

    en.wikipedia.org/.../Distance_from_a_point_to_a_line

    The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original ...

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