几何代数

量子纯态与混合态的几何代数分析

Geometric Algebra Analysis of Quantum Pure State and Mixed State

几何代数是在Clifford代数的基础上，建立的一种更具概括性数学语言。

Geometric algebra is a more general mathematical language established on the basis of the Clifford algebra .

将信号稀疏表示理论和THz-TDS信号几何代数分析的研究结果相结合，对THz-TDS信号矢量进行基于冗余字典的稀疏表示，提出了基于稀疏表示的THz-TDS信号分类方法。

From the signal sparse representation and the results of the THz-TDS analysis , THz-TDS signal vectors can be sparsely represented in an overcomplete dictionary , anda signal classification method via the sparse representation is presented .

利用几何代数进行线段模型匹配和运动估计

Matching and Estimating Motion of Line Model Using Geometric Algebra

基于共形几何代数的圆拟合方法实现

Realization of Circle Fitting Algorithm Based on Conformal Geometric Algebra

以往的数学史家多用几何代数观点来解释这个问题。

Past mathematicians explained it with the so-called geometric algebra .

共形几何代数&几何代数的新理论和计算框架

Conformal Geometric Algebra & A New Framework for Computational Geometry

电磁场方程微分形式的另一种导出方式以及它的几何代数形式

Differential forms and geometrically algebraic forms of Maxwell 's equations

共形几何代数与几何不变量的代数运算

Conformal Geometric Algebra and Algebraic Manipulations of Geometric Invariants

共形几何代数与运动和形状的刻画

Conformal Geometric Algebra for Motion and Shape Description

几何代数及其在飞行力学中的应用

Geometric Algebra and Its Usage in Flight Dynamics

Heoom又把不少希腊的几何代数法翻译成算术和代数步骤。

Heron also translated much of the Greek geometrical algebra into arithmetic and algebraic processes .

几何代数在定理证明中的消元与化简算法

Algorithms of elimination and simplification based on geometric algebra in automatic proving of geometric theorem

本文应用共形几何代数分析串联机器人的运动学反解。

This paper applies conformal geometric algebra to analyze the reverse kinematics of serial robot .

本文尝试将共形几何代数理论引入V-邻域算法构建中。

This paper tries to introduce conformal geometric algebra for the building of V-Construction neighborhood algorithm .

共形几何代数是一个新的几何表示和计算工具。

Conformal Geometric Algebra ( CGA ) is a new tool for geometric representation and computation .

分析表明采用几何代数与采用四元数代数在解决三维线性变换的统一推导问题方面，数学描述等价。

The mathematics expressions of using geometric algebra to solve the unified driving of linear transformations are equal to those of quaternion algebra .

通过对卡诺结构多维性的分析讨论，推介一种新的几何代数算法，并充分论证其正确性和有效性。

Through commenting on the multiple dimensional character of Karnaugh structure , a new algebra-geometry algorithm with its correctness and efficiency is presented .

本文在分析了矩阵代数、向量代数和四元数代数进行三维线性变换推导的基础上，采用几何代数，研究了三维线性变换的统一推导公式。

By analyzing the deriving methods of matrix , vector algebra and quaternion algebra , a unified deriving formula of linear transformations is presented by using geometrical algebra .

现在将要使用的一个新的数学系统是几何代数，尤其是五维共形几何代数，它统一了过去使用的各种数学系统，能够以简便和富有几何直观的方式应用于我们的问题中。

Now , we will want to use another system is geometric algebra , in particular the five-dimensional conformal geometric algebra , it unifies mathematical systems used computer graphics in a simple and intuitive way .

作为几何代数的子集，对偶四元数是刻画一般性刚体运动的最简洁、最有效的数学工具，可以用来研究包括惯性导航在内的所有刚体运动学（和动力学）问题。

As a subset of geometry algebra , dual quaternion is the most concise and efficient mathematical tool to represent the general rigid motion . It can be used to address all rigid kinematic ( and dynamic ) problems , including inertial navigation of course .

这种方法构造的准循环LDPC码比纯几何或代数方法要更为灵活。

It is more flexible to construct QC-LDPC than pure geometric or algebraic methods .

自H.Hopf研究紧李群同调时提出了Hopf代数概念之后，人们发现它与李代数、微分几何、代数拓扑及统计物理具有广泛的联系。

When H.Hopf studied the homology of compact Lie group , he gave the concept of Hopf algebra .

利用LerayHirsch性质，对于紧单李群G的旗流形，讨论了其上映射的Lefshetz数的计算，并给出了一些几何和代数中的应用。

It is discussed that the computation of Lefschetz numbers of maps on flag manifolds of compact simple lie G by using Leray-Hirsch property . Some applications in geometry and algebra are given .

在三维欧氏空间中，作为特殊曲线，Mannheim曲线、Bertrand曲线以及一般螺线具有良好的几何和代数性质.讨论了三维欧氏空间中特殊曲线的主法线曲面。

Discusses algebraically and geometrically the properties of the ruled surfaces in the Euclidean three-space , especially , the principal normal surfaces on which there are some special curves , such as Mannheim curves , Bertrand curves and general helices .

当k≥2时，k-Hessian方程是一类复杂的完全非线性方程，对它的研究又是很有挑战的，需要深入了解几何，代数，分析，偏微分方程等各个领域的知识。

The k-Hessian equation is a kind of very complicated fully nonlinear partial differential equation when k ≥ 2 . It is a hard job to study the equation which need a wide knowledge , such as geometry , algebra , analysis , partial differential equations and so on .

（数学）用几何和代数的方法或从属之的。

( math ) using or subjected to a methodology using algebra and calculus .

它由两个方面发展而来，代数几何和代数数论。

It has developed from two sources : algebraic geometry and algebraic member theory .

从而介绍了解析几何向量代数部份的两种新体系。

So we introduce two Kinds of system for vector algebra section of analytic geometry .

我的几何和代数只是勉强及格。可是，她这两门课在班里都是第一。

I barely passed algebra and geometry , but here she 's head of her class in both .