# Euclidean norm

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## Euclidean norm

(mathematics)
The most common norm, calculated by summing the squares of all coordinates and taking the square root. This is the essence of Pythagoras's theorem. In the infinite-dimensional case, the sum is infinite or is replaced with an integral when the number of dimensions is uncountable.
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Particularly, in our proposed work (SE), there is about 0([M.sup.2]) for computation of the Euclidean norm, division of each entry of a row by its corresponding Euclidean norm and summing all the scaled-energy values to get the final test statistic [T.sub.SE] .
Face motion [F.sub.6] Average value of the Euclidean norm of a set of landmarks in the last N frames.
It is worth mentioning that we chose the Euclidean norm because it is the natural norm associated with the dot-product that measures the similarity between objects.
We compared and analyzed several key parameters such as the convergence generation number of the average fitness curve, the normalized Euclidean distance between the average fitness value and the optimal fitness value after reaching the convergence generation number, the median value, the maximum, the mean value, and total Euclidean norm of error vector with 200 generations in the average fitness curve.
Save [S.sub.R]; While (Euclidean Norm is Not Min.) TURN in-place; // rotate CCW Capture measured scan ([mathematical expression not reproducible]); OutLierFilter([mathematical expression not reproducible]); [D.sub.i] [left arrow] CalcEuclideanNorm([S.sub.R], [mathematical expression not reproducible]); //calculate Euclidean Norm between ref.
Since [??] and [??] are complex while gamma is constrained to be real (and nonnegative), the Euclidean norm used by McCulloch [13] and Nolan et al.
where [parallel]d[parallel] indicates the Euclidean norm of a vector d.
The simplest and probably most popular clustering [9, 49] model is k-means [33, 34] which can be formulated as a p-median problem (2) where [w.sub.i] = 1 [for all] = [bar.1, N] and L(x) is squared Euclidean norm [l.sub.2]:
where [parallel]x[parallel] is the Euclidean norm given by [parallel]s[parallel] = [square root of [s.sup.2.sub.1] + ...
There exists [T.sub.1] > [t.sub.0] such that [parallel][x.sub.i](t) - [x.sub.j](t)[parallel] [less than or equal to] [epsilon], where t > [T.sub.1], i, j = 1, 2, ..., N, and [parallel] * [parallel] denotes the Euclidean norm.
In [1] and [2] the formulae for the determinant, eigenvalues, Euclidean norm, spectral norm and inverse of the right circulant matrices with arithmetic and geometric sequences were derived.
The goal of the QICLCMP beamformer is to impose an additional quadratic inequality constraint on the Euclidean norm of w for which the purpose is to improve the robustness to pointing errors and to random perturbations in sensor parameters.

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