# Orthogonal projection

## Definitions

• Webster's Revised Unabridged Dictionary
• Orthogonal projection See under Orthographic.
• Orthogonal projection that projection which is made by drawing lines, from every point to be projected, perpendicular to the plane of projection. Such a projection of the sphere represents its circles as seen in perspective by an eye supposed to be placed at an infinite distance, the plane of projection passing through the center of the sphere perpendicularly to the line of sight.
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## Usage

### In science:

If ν is a positive linear functional then sν is its support projection, the smallest orthogonal projection P such that ν (1 − P ) = 0.
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Quantum hypothesis testing is set with respect to a sequence of ﬁnite dimensional orthogonal projections pn on h such that s − limn pn = 1.
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
It follows that s′ω = J sω J ∈ M′ is the orthogonal projection on the closure of MΩω .
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Therefore, as t ↑ ∞, the states ωt are concentrating exponentially fast along the projections s(ωt−ω−t )+ while the states ω−t are concentrating exponentially fast along the orthogonal complement 1 − s(ωt−ω−t )+ .
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
The orthogonal projection 1R onto hR coincide with the projection onto the absolutely continuous part of h0 .
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
Let P j : J → J (e j , 1) be the orthogonal projection on J (e j , 1).
Maximal Invariants Over Symmetric Cones
In this study, we have devised an orthogonal fault classiﬁcation scheme and calculated their frequencies over seven open source Java projects.
Towards a better understanding of testing if conditionals
In the sequel, (cid:98)Πk stands for the orthogonal projection in Rn onto the reason, we propose a Fisher-type statistic. space generated by the ˆkKL columns of W.
Minimax adaptive tests for the Functional Linear model
Furthermore the orthogonal projection of S near y on any coordinate line xj contains a neighborhood of yj .
Sampling From A Manifold
Let ΠSF f and ΠS c f be the orthogonal projections of a function f ∈ Σ on span(cid:0){ϕl }l∈SF (cid:1) and span(cid:0){ϕl }l∈S c F (cid:1) respectively.
Minimax testing of a composite null hypothesis defined via a quadratic functional in the model of regression
Let P be an orthogonal projection, rankP = k .
John decompositions: selecting a large part
Let P be an orthogonal projection, rankP = k .
John decompositions: selecting a large part
For any set A ∈ Ed , A|F denotes the (orthogonal) projection of A onto F ∈ Lj,d.