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Projection (linear algebra)
Idempotent linear transformation from a vector space to itself / From Wikipedia, the free encyclopedia
"Orthogonal projection" redirects here. For the technical drawing concept, see Orthographic projection. For a concrete discussion of orthogonal projections in finite-dimensional linear spaces, see Vector projection.
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] 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.
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