Particularly,  (Volume Detector, VD) uses the determinant of a SCM by first dividing each entry of a SCM with their corresponding row's Euclidean norm
. Whereas,  (Hadamard Ratio Test) uses a ratio of the determinant of a SCM to a product of diagonal entries of a SCM.
In the CODAS method, when two alternatives have higher similarity in the Euclidean norm
, the second criterion--i.e., the Hamming distance--is used as the basis of comparison.
where is the amount of frames to include in the motion analysis, D(i, j) is the jth element of [A.sub.i] [member of] D, f is the number of the current frames, and [parallel]*[parallel] is the Euclidean norm
. In our analysis, we used Z = 50 (50 frames, equivalent to 1 second).
Since the error functional is a twice differentiable function, hence the second-order Taylor series can be used as [m.sub.k] model of J; as the norm, we are using the Euclidean norm
Here, [absolute value of x] is the usual Euclidean norm
. Using this observation, and (14), we obtain the following (for this special case).
The variation tolerance step normalizes the palmprint features using Euclidean norm
reducing the variations of features values due to changes in illumination, shadowing, and orientations.
Therefore, it is not reasonable to compare the Euclidean norm
error between the optimal fitness value and the average fitness value after convergence, because it is difficult to express the merits and demerits of each algorithm.
At each angular position, the measured scan ([S.sub.M]) is compared, by calculating the Euclidean norm
(also known as the square root of the sum of squares of differences), with already stored reference scan and the one which gives the minimum Euclidean distance ([D.sub.i]) is assumed to be the closest angular position with the reference orientation (facing staircase).
Inspired by the development of sparse optimization methods, in this paper, a sparse optimization model with the [l.sub.0]-norm and the squared Euclidean norm
as the objective function is built to maximize the utilization of the regenerative braking energy.
For an initial guess [x.sub.0] [member of] [C.sup.n], GMRES  approximates the exact solution of Ax = b at step k by the vector [x.subg.k] [member of] [x.sub.0] + [K.sub.k] (A, [r.sub.0]) that minimizes the Euclidean norm
of the residual [r.sub.k] = b - A[x.sub.k], i.e.,
where [(x).sup.H] is the conjugate transpose operator and [parallel] x [parallel] denotes the Euclidean norm
. [mathematical expression not reproducible] is a truncated version of the target steering vector, while [mathematical expression not reproducible] truncated versions of the steering vectors [a.sub.d]([f.sub.t]), [a.sub.r]([[theta].sub.t]), and [a.sub.t] ([[theta].sub.t]), respectively.