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''P''::nowrap    ''U''::mathrm    Space::bmatrix    ''u''::langle    Rangle::vector    Begin::matrix

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The transformation P is the orthogonal projection onto the line m.

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P2 = 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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