a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional

therefore, these points are 「homogeneous」 because they represent the same point in euclidean space (or cartesian space).

因此这些点是「齐次」的，因为他们始终对应于笛卡尔坐标中的同一点。

it is revealed that the paradox solution in euclidean space is just a solution in symplectic space in the jordan form which can easily be obtained by conventional mathematical means.

本文的工作表明，欧几里得空间下的佯谬解就是辛空间下的约当型解，而且通过标準的数学方法可以直接获得所有佯谬问题的解析解。

in this paper, we give the sets of radii which make the measures of balls and spheres finite but not infinitesimal respectively, in a euclidean space of infinite dimension.

本文分别给出了使在无穷维欧氏空间中球体和球面具有有限的，但又不是无穷小的测度的半径集合。

in the euclidean space of the locally rings, the expresson of the orthogonal transformation with symmetry is one of the basic problems on the rings of eucliden geometry.

局部环上欧氏几何中，正交变换表为对称问题，是环上欧氏几何的基本问题之一。

the finite temperature and chemical potential axial anomalies in euclidean space are studied within the framework of perturbation theory.

本文从微扰理论出发研究欧氏空间中有限温度和有限化学势下的轴反常。

a nonexistence theorem is established for f-harmonic map with finite f-energy from euclidean space to any riemannian manifold.

建立了从欧氏空间到任何黎曼流形的具有有限f-能量的f-调和映照的非存在性定理。

distance-based and density-based clustering algorithms in euclidean space can be used in this framework.

欧几里德空间内基于距离、基于密度的聚类算法均适用于本框架。

a new technique to design polynomial time approximation schemes(ptas) for np hard problems in euclidean space is introduced.

提出了一种在欧氏平面上设计多项式时间近似方案的新技术。

furthermore, a conjecture on further generalization to higher dimension case or general euclidean space is proposed which requires further study.

这一不等式可能推广于更高维或一般的欧氏空间中，有待进一步研究。

you all have a sense of what a flat space is, euclidean space is.

大家都多少知道平面空间是什么，就是欧几里德空间。

the real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional euclidean space are studied.

研究实对称矩阵、对角矩阵以及欧氏空间的规范正交基。

it gives the decision conditions of linear transformation under euclidean space and some natures of special linear transformation.

借助内积关系 ，给出了欧氏空间的变换是线性变换的两个充要条件 ，并由此得到一些相关结论 。