# Orthogonal Projection

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Related to Orthogonal Projection: orthographic projection, Perspective projection

## orthogonal projection

[ȯr′thäg·ən·əl prə′jek·shən]
Also known as orthographic projection.
(graphic arts)
A two-dimensional representation formed by perpendicular intersections of lines drawn from points on the object being pictured to a plane of projection.
(mathematics)
A continuous linear map P of a Hilbert space H onto a subspace M such that if h is any vector in H,h= P h+w, wherewis in the orthogonal complement of M.
A mapping of a configuration into a line or plane that associates to any point of the configuration the intersection with the line or plane of the line passing through the point and perpendicular to the line or plane.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Orthogonal Projection

a particular case of parallel projection in which the axis or plane of projection is perpendicular (orthogonal) to the direction of projection.

References in periodicals archive ?
The orthogonal projection [P.sub.M,I] : [L.sup.2](I) [right arrow] [V.sub.M](I) is defined by
We now give the formulation of orthogonal projection [P.sub.C] where C is a simply closed convex sets as follows, and in the case that C is not a simply closed convex sets, for instance, C is a halfspace, we can found more the formulation in .
At the same time, SIMPCA estimation results are better than SOPIM estimation results, mainly because Column weighting for SIMPCA is introduced, while SOPIM uses orthogonal projection only.
Suppose there exists a reducing subspace [mathematical expression not reproducible] denote the orthogonal projection from [([K.sup.2.sub.u]).sup.[perpendicular to]] onto M.
Therefore, an orthogonal projection matrix [O.sub.p] can be defined to identify any spectra in the corresponding data set Y of the sample profiles that are related to those in X.
(ii) Every element x [member of] X admits at most one orthogonal projection [P.sup.[perpendicular to].sub.H] (x) onto H.
It follows that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the orthogonal projection. Since [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we conclude that [P.sub.T]([x.sub.k]) [right arrow] [[pi].sub.N'] [omicron] [DX.sub.T]([sigma])[|.sub.N] as k [right arrow] [infinity].
If we restrict f to be in [L.sup.2](0, 1), then [Q.sub.n]f is exactly the orthogonal projection of [L.sup.2](0,1) onto [[DELTA].sub.n] [subset] [L.sup.2](0,1) under the [L.sup.2]- norm [[parallel]f[parallel].sup.2] = [square root of ([[integral].sup.1.sub.0] [[absolute value of (f)].sup.2]dm)] of [L.sup.2](0,1).
Consider the orthogonal projection G' of G onto [H.sub.xy].
For the right-hand GUI widget, I create a cube (made square through the orthogonal projection).
For accuracy analysis, orthogonal projection and nonorthogonal projection were considered.

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