Euclidean space

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Euclid′ean space′


n.
ordinary two- or three-dimensional space.
[1880–85]
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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
Translations
euklidovský prostor
espacio euclideoespacio euclídeoespacio euclidiano
euklidinen avaruus
euklidski prostor
ユークリッド空間
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].