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quaternions
相关语句
  四元数
     Let H~(m×n)denote the set of all m×n quaternions matrices,let δ_1(A)≥… ≥δ_n,(A) be the singular values of A∈H~(m×n).
     设 H~(m×n)为 m×n 四元数矩阵的集合,σ_1(A)≥…≥σ_n(A)为 A∈H~(mxn)的奇异值。
短句来源
     Let P be the affine group of the real line R, and let H be the set of all quaternions.
     设P是实直线R上的仿射群,H为所有四元数的集合。
短句来源
     Probability Analysis of the Rounding Error in the Computation of the Quaternions
     四元数计算舍入误差的概率分析
短句来源
     Applications of Grbner Bases in Polynomial Rings over the Division Ring of Real Quaternions
     四元数除环上多项式环的Grbner基的应用
短句来源
     Let λ0 be a real number, X be a vector, then the numbers in the form of λ0+λ are referred to as hypercomplex numbers or quaternions.
     设λ_0为实数,λ为矢量,形如λ_0+λ的数称为超复数或四元数
短句来源
更多       
  四元数法
     The paper interprets the basic principle of registration in computer integrated surgical systems and technology ,and presents an ICP(Iterative Closest Point ) algorithm based on contour feature ,which combines the advantages of the ICP analytical optimization and the quaternions to solve the problem of image contour points registration?
     介绍了计算机集成外科手术系统中空间配准的基本原理,提出了基于轮廓特征的ICP配准算法。 这种算法结合了ICP最优化解析方法和四元数法的优点,解决了图像轮廓点的空间配准问题。
短句来源
     Three parameters are applied of unit quaternions method as optimizing space, and global rough registration between the CAD modeling data and the 3D measured data is obtained.
     利用遗传算法具有全局搜索能力的特点 ,以四元数法中的 3个参量作为优化解空间 ,采用自适应控制优化参数的方法 ,达到 CAD模型数据和三维测量数据点的全局粗配准。
短句来源
     Quaternions are used to describe the attitude of the rigid body system in this paper.
     采用四元数法描述了刚体姿态系统。
短句来源
     SINS is calculated by quaternions and the in-tegrated navigation system is simulated by federated Kalman fil-tering method in this paper.
     本文采用四元数法进行SINS计算,并运用联邦滤波的方法对组合导航进行了仿真。
短句来源
  “quaternions”译为未确定词的双语例句
     This paper proves that the multiplicative complexty of any algebraof finite dimension is equal to the united rank of matrices C_k which con-sist of the algebra's structure constants. For the multiplicative complex-ity πA of algebra of quaternions over any field,we prove that 7≤πA≤9.This improves the latest result 7≤πA≤10.
     本文证明了有限维代数的乘法复杂度等于其结构常数确定的矩阵 CK 的联合秩,并对于四元代数的乘法复杂度πA,由现有的结果7<πA<10,改进为7≤πA≤9.
短句来源
     (Q) denote the set of all n×n self-conjugate quaternions matrices. Suppose that λ (A) (s=1, 2. …, n) are eigenvalues for A∈SC, (Q), where λ_1(A)≥…≥λ_n(A).
     本文证明了 1)如果A∈SC_n(Q), P∈Q~(n×n) ,则 sum from s=1 to k(λ_(n-s-1)(PAP~n))≤sum from s=1 to k(λ_s(A)λ_s(PP~n)), k=1,2,. .
短句来源
     We give an affirmative answer to the open problem proposed by Dr, Fuzhen Zhang in the paper "Quaternions and matrices of quaternious"( LA A251:21-57 ) ,that is, there exists a 2n × 2n complex matrix B such that, for any n×n complex matrices A1, A2
     给出了文[1]中一个公开问题的肯定回答,即对任意的 n × n复矩阵 A1,A2存在 2n × 2n复矩阵 B,使得,
短句来源
     Using Real Quaternions to Represent Rotation in Three Dimensions
     实四元数组与三维旋转
短句来源
     A Public-key Cryptography Using Integral Quaternions
     一种四元整数公钥密码体制
短句来源
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  quaternions
The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitatio
      
The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitatio
      
The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitatio
      
Analysis of optimal motion control for a material point in a central field with application of quaternions
      
Dimension formula of cusp form spaces on half-spaces of quaternions
      
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Let λ0 be a real number, X be a vector, then the numbers in the form of λ0+λ are referred to as hypercomplex numbers or quaternions. This paper contains two parts:1.Algebraic operations of quaternion are defined by utilizing the knowledge in vector algebra and the fundamental properties of algebra of quaternions are derived.2.Rotation of a rigid body about one fixed point is described in algebra of quaternions.

设λ_0为实数,λ为矢量,形如λ_0+λ的数称为超复数或四元数。本文包含两个部分: 1.用矢量代数的知识定义四元数的代数运算,导出四元数代数的基本性质; 2.用四元数描述刚体绕固定点的转动。

Let K be any skew-field with central field F. A matrix A=(a_ij)n×n over K is called centralized if the characteristic matrix λI-A can be reduced by some elementary transformations into the following diagonal form:such that are all manic polynomials over F.The determinant of a centralized matrix A=(a_ij)n×n may be defined by (1) asfollows:and then the famous theorem of Hadamard can be generalized as in the following:Theorem. If A=(a_ij)n×n is a non-singular centralized matrix over the skewfield of quaternions,...

Let K be any skew-field with central field F. A matrix A=(a_ij)n×n over K is called centralized if the characteristic matrix λI-A can be reduced by some elementary transformations into the following diagonal form:such that are all manic polynomials over F.The determinant of a centralized matrix A=(a_ij)n×n may be defined by (1) asfollows:and then the famous theorem of Hadamard can be generalized as in the following:Theorem. If A=(a_ij)n×n is a non-singular centralized matrix over the skewfield of quaternions, thenand the equality sign holds if and only if the columns of A are all muturally orthogonal.This theorem may be proved by the following three lemmas:Lemma 1. If A is a centralized n-rowed square matrix of quaternions, then sois andLemma 2. For any n-rowed square, matrix A of quaternions, the. following two matrices are always centralized:andLemma 3. If A is a centralized matrix of quaternions, then we have

本文是把实数域上著名的Hadamard定理推广到四元数体上,而得到下列结果:如果A=(a_(ij)n×n为四元数体上可中心化的非奇异矩阵,则有且等号成立的充要条件为A的各行是广义正交的。

In this paper the following theorerms and propositions are proved:1°For any self-conjugate matrix A of rank γ over the skew-field of quaternions there exists a left tall matrix L such that L'AL is a γ-rowed non-singular self-conjugate matrix;2°Unique decomposition theorem of positive definite matrix;3°A determinant of a self-conjugate matrix is not changed in value under the GH-congruence trasformations;4°Some equivalent propositions about positive definite matrices and semi-positive definite matrices.

本文证明了下面一些定理与命题: 1°对四元数体上任意秩数为r的自共轭矩阵A恒存在一个左高矩阵L使得为一个r阶的非奇异自共轭矩阵; 2°正定矩阵的唯一分解定理; 3°自共矩矩阵的行列式在GH合同变换下不变值; 4°关于正定矩阵与半正定矩阵的一些等价命题。

 
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