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The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. [1]
The trace of a Hermitian matrix is real, because the elements on the diagonal are real. The trace of a permutation matrix is the number of fixed points of the corresponding permutation, because the diagonal term a ii is 1 if the i th point is fixed and 0 otherwise. The trace of a projection matrix is the dimension of the target space.
As one example, if there is free space between the two planes, the ray transfer matrix is given by: = [], where d is the separation distance (measured along the optical axis) between the two reference planes.
Mil-dot reticle as used in telescopic sights. • If the helmeted head of a man (≈ 0.25 m tall) fits between the fourth bar and the horizontal line, the man is at approximately 100 meters distance. • When the upper part of the body of a man (≈ 1 m tall) fits under the first line, he stands at approximately 400 meters distance.
Given a function :, the associated trace function on is given by = (), where has eigenvalues and stands for a trace of the operator. Convexity and monotonicity of the trace function [ edit ]
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Lemma 1. ′ =, where ′ is the differential of . This equation means that the differential of , evaluated at the identity matrix, is equal to the trace.The differential ′ is a linear operator that maps an n × n matrix to a real number.
In mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent of the choice of basis used to compute the trace. This trace of trace-class operators generalizes the trace of matrices studied in linear algebra.