Euclidean space

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Euclid′ean space′

ordinary two- or three-dimensional space.
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Noun1.Euclidean space - a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
metric space - a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
euklidovský prostor
espacio euclideoespacio euclídeoespacio euclidiano
euklidinen avaruus
euklidski prostor
euklidiskt rum
References in periodicals archive ?
Finally, obtain the accurate or approximate solution of x, which is based on a strict mathematical optimization problem: min[[parallel]y - [PHI][[PSI].sup.T]x[parallel].sub.2] + [lambda][[parallel][[psi].sup.T]x[parallel].sub.0], where [[parallel] [parallel].sub.2] and [[parallel] [parallel].sub.0] is the 2-norm and 0-norm, respectively.
Furthermore, error 2-norm of first-order natural frequency is also shown in Table 6.
If the matrix B is full rank, then [parallel]([I.sub.n] - [BB.sup.+])E[parallel] [less than or equal to] [parallel]E[parallel] where the operator [parallel]*[parallel] denotes the 2-norm of the matrix *.
(Necessarily, d = 0 because the result is a norm and therefore positive homogeneous.) In the special case where \\ * \\ [DELTA] and \\ * \\ [DELTA] are both the 2-norm, then [A.sub.i], [b.sub.i], [B.sub.i], and [K.sub.i] are given by (2.3) in Example 2.2.
where {[??]} is scaled by its 2-norm because [V] is a unit orthogonal matrix.
where [parallel] x [parallel] denotes the 2-norm and [parallel][([[??].sub.r]).sub.max][parallel] = [parallel][y.sub.d] - [y.sub.0][parallel]/[tau] is the maximum value of [[??].sub.r] which is obtained from (3), where [DELTA]y = [parallel][y.sub.d] - [y.sub.0][parallel] is the difference between initial and desired values of the output.
Usually, matrix infinite norm is larger than matrix 2-norm; thus the result established in Theorem 5 can be rewritten by matrix 2-norm form further.
Hence, the 2-Norm of the estimation lingering of [z.sub.a] is
where [[phi].sub.u] is the time length center, ||[s.sub.p]|| is the 2-norm of [s.sub.p], and [[phi].sub.u] can be gotten by:
The iteration stops when the Euclidean norm (2-norm) of the residual vector is reduced by [10.sup.-14].
In order to assess the quality of the calibration process, it was used the 2-norm condition number of the first matrix in Equation (2) as:
The theory of probabilistic normed spaces was initiated and developed in [1], [17], [31], [32] and further it was extended to random/probabilistic 2-normed spaces [8] by using the concept of 2-norm [7].