## ::Projection (linear algebra)

### ::concepts

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In linear algebra and functional analysis, a **projection** is a linear transformation *P* from a vector space to itself such that *P*^{2} = *P*. That is, whenever *P* is applied twice to any value, it gives the same result as if it were applied once (idempotent). It leaves its image unchanged.<ref>Meyer, pp 386+387</ref> Though abstract, 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.

**Projection (linear algebra) sections**

Intro Simple example Properties and classification Canonical forms Projections on normed vector spaces Applications and further considerations Generalizations See also Notes References External links

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