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Projection Operator




In Mathematics , a projection operator ''P'' on a Vector Space is a Linear Transformation that is Idempotent , that is, ''P''2 = ''P''. Such transformations ''project'' any point in the vector space to a point in the subspace that is the image of the transformation.

Intuitively, a projection operator "picks out" entries in a vector, for example,

: p_{1,3,4} \begin{pmatrix} 3 \ 97 \ \pi \ -17.73 \ 10^{10^{10}} \end{pmatrix} = \begin{pmatrix} 3 \ 0 \ \pi \ -17.73 \ 0\end{pmatrix}.


In Physics , the term ''projection operator'' usually means '' Self-adjoint projection operator''.

The only possible Eigenvalue s of a projection operator over a finite-dimensional real or complex vector space are 0 and 1.