: Mathématiques: projection

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projection

In linear algebra and functional analysis, a projection is a linear transformation ${\\displaystyle P}$ from a vector space to itself (an endomorphism) such that ${\\displaystyle P\\circ P=P}$ . That is, whenever ${\\displaystyle P}$ is applied twice to any vector, it gives the same result as if it were applied once (i.e. ${\\displaystyle P}$ is idempotent). It leaves its image unchanged. This definition of "projection" formalizes and generalizes the idea of graphical projection. One can also consider the effect of a projection on a geometrical object by examining the effect of the projection on points in the object.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Projection_(linear_algebra))

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