例如欧氏空间在旋转和平移下都不会改变。
For example, Euclidean space is invariant under rotations and translations.
第三章，我们考虑了欧氏空间上的退火过程。
In the third chapter, we discuss the annealing process on the Euclidean space.
研究实对称矩阵、对角矩阵以及欧氏空间的规范正交基。
The real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional Euclidean space are studied.
论述欧氏空间、辛空间、伪辛空间的本质属性及演变过程 。
The essential property and developmental course of Euclidean space, symplectic space and bogus symplectic space are studied.
利用长度关系给出了欧氏空间的变换为对称变换的若干个充要条件。
A few good necessary and sufficient conditions are given by using length relation for symmetrical transformation on Euclidean space.
借助内积与长度与夹角给出了欧氏空间的变换是反对称变换的若干个充要条件。
A few good necessary and sufficient conditions are given by using inner product and length relation for antisymmetric transformation on Euclidean space.
借助内积与长度与夹角给出了欧氏空间的变换是反对称变换的若干个充要条件。
A few good necessary and sufficient conditions are given by using length relation for symmetrical transformation on Euclidean space.
镜面反射是欧氏空间中一类很重要的线性变换，在几何空间中有着极其形象的解释。
The specular reflection is a very important linear transformation in Euclidean space, and it has a special geometrical explanation in geometrical space.
在n维欧氏空间内，给出了多元函数分别关于点、n-1维超平面对称的充要条件。
Necessary and sufficient conditions are given on the symmetry of points and n-1 dimensional hyperplane of function of many variables in then-dimensional Euclidean space.
得到了欧氏空间中，单位球面上坐标函数关于某一特定标架场的协变微分的两个等式。
We obtain two formulas about the covariant derivative of the coordinate functions on the unit sphere in Eucdidean space.
实验结果表明此方法可以在近似欧氏空间中从两幅图像重建外科手术场景和手术对象。
The results showed that this method could be used to reconstruct the surgical scene in a close Euclidean space.
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。
By the relation transvection, we obtain two necessary and sufficient conditions for the transformation being linear transformation in Euclid Spaces, and out of it, we have got some conclusions.
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 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.
在欧氏空间中复杂网络可以是有形物体，如电力网、互联网、高速公路或地铁系统、甚至神经网络等等。
Complex network can be tangible objects in the Euclidean space, such as electric power grids, the Internet, highways or subway systems, and the neural network.
经典微分几何研究三维欧氏空间中曲线曲面理论，其最具有特色的研究是主曲率函数满足某些关系的魏因加吞曲面。
In the classical differential geometry which deals with the theory of curves and surfaces of three dimensional Euclidean space, the most distinctive study is the Weingarten surface.
应用微元法给出了在三维欧氏空间中质量曲线和质量立体对任意一条直线的转动惯量的计算公式，并给出了对坐标轴的转动惯量的简化计算公式。
Via an infinitesimal method, the author offers a computing formula for the moment of inertia of mass curves and mass cubes against any straight line in Euclidean space.
采用空间点到点欧氏距离公式实现特征点处软组织厚度的快速测量。3颅面复原知识库构建及知识推理策略制定。
Then a fast measurement was achieved by calculating the Euclidean distance between points. 3 Constructing the knowledge base and inference strategy.
本文在比较分形几何和欧氏几何的基础上，试图从分形的“自相似”角度来探究建筑空间形式的相关问题。
Based on the comparison of fractal geometry and Euclidean geometry, on the basis of geometric from fractal "similar" perspective building space forms of related problems.
本文在比较分形几何和欧氏几何的基础上，试图从分形的“自相似”角度来探究建筑空间形式的相关问题。
Based on the comparison of fractal geometry and Euclidean geometry, on the basis of geometric from fractal "similar" perspective building space forms of related problems.
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