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Projection formula. In algebraic geometry, the projection formula states the following: [1] [2] For a morphism of ringed spaces, an -module and a locally free -module of finite rank, the natural maps of sheaves. are isomorphisms. There is yet another projection formula in the setting of étale cohomology .
For more general concepts, see Projection (linear algebra) and Projection (mathematics). 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 or a∥b .
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 ...
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In linear algebra and functional analysis, a projection is a linear transformation from a vector space to itself (an endomorphism) such that . That is, whenever is applied twice to any vector, it gives the same result as if it were applied once (i.e. is idempotent ). It leaves its image unchanged. [1]
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection ), onto a plane (the projection plane) perpendicular to the diameter through the point. It is a smooth, bijective function from the entire sphere except the center of projection to the ...
v. t. e. In technical drawing and computer graphics, a multiview projection is a technique of illustration by which a standardized series of orthographic two-dimensional pictures are constructed to represent the form of a three-dimensional object. Up to six pictures of an object are produced (called primary views ), with each projection plane ...
In statistics, the projection matrix , [1] sometimes also called the influence matrix [2] or hat matrix , maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes the influence each response value has on each fitted value. [3] [4] The diagonal elements of the projection ...