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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 ...
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 .
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 .
In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .
In relational algebra, a projection is a unary operation written as ,..., (), where is a relation and ,..., are attribute names. Its result is defined as the set obtained when the components of the tuples in R {\displaystyle R} are restricted to the set { a 1 , . . . , a n } {\displaystyle \{a_{1},...,a_{n}\}} – it discards (or excludes ) the ...
In mathematics, the scalar projection of a vector on (or onto) a vector , also known as the scalar resolute of in the direction of , is given by ...
Enjoy a classic game of Hearts and watch out for the Queen of Spades!
The natural projection on the tangent bundle on a manifold. The unary operation of projection in relational ... Using the mathematical symbols to display words (or ...