四元数

四元数Beta分布、F分布及其特征根分布

Quaternion beta distribution , distribution and their latent roots ' distribution s

四元数矩阵的Jordan标准形

Jordan Canonical Forms of Matrices over Quaternion Field

基于四元数和B样条的机械手平滑姿态规划器

Smooth orientation planner for manipulators based on quaternion and B-spline

四元数在GPS船姿测量中的应用

Application of quaternion algorithm in GPS-based ship attitude determination

基于四元数方法的GPS航姿解算

GPS based Attitude Determination Based on Quaternion Algorithm

设P是实直线R上的仿射群，H为所有四元数的集合。

Let P be the affine group of the real line R , and let H be the set of all quaternions .

关于四元数EP矩阵偏序的研究

On Partially Ordered EP Matrix Over Quaternion Field

四元数方阵的GH合同标准形与同时对角化

GH - congruence Canonical Form of Quaternion Matrix and Simultaneous Diagonalization of Matrices

再使用四元数Gabor滤波器组进行解析特征提取；

Second , a quaternionic Gabor filter bank was designed to extract analytic features ;

一类四元数函数和Maxwell方程

A class of quaternion functions and Maxwell equation

在这方面，四元数（Quaternion）的理论和方法或许是合适的。

In this aspect , the quaternion theories and methods perhaps are appropriate .

四元数体上方阵的广义GH变换及应用

The Generalized GH-Transformations of Square Matrice Over the Division Ring of Quaternions and its APPlications

介绍了修正罗德里格参数（MRP），分析比较了姿态表示参数修正罗德里格参数和四元数的算法特点。

Analyzed and compared both MRP and quaternion algorithms ' characteristics by ( simulations ) .

基于EMD细化四元数谱的纹理分割

Texture segmentation using EMD refined quaternionic spectrum

给出了〔5〕中Hamilton四元数环的一种构造方式；

It gives a way of producing Hamilton 's quaternions ring that is given by [ 4 ] ;

利用四元数表达计算出旋转参数R和平移参数t，完成配准工作。

The run time is shorten as well . Adopting quaternion expression , this paper has computed the rotation parameter R and the translation parameter t to realized registration .

本文基于旋转矩阵单位四元数分解定理，提出一种由3D特征点空间位置估计运动参数的算法。

Based on the unit quaternion decomposition of rotation matrix , this paper puts forward an algorithm to estimate motion parameters from the space position vectors of 3D feature points .

Minkowski不等式在四元数矩阵中的推广

The generalization of Minkowski inequality to matrix of quaternion elements

复四元数与狭义Lorentz群

Complex Quaternion and Restricted Lorentz Group

四元数体上广义Toeplitz矩阵反问题

Inverse Problem for Generalized Toeplitz Matrices over Quaternion Field

四元数体上矩阵的对角化和Schur定理（英文）

On Diagonalization of Matrices and Schur Theorem over Quaternion Field ;

四元数体上任意矩阵的UR分解

The UR decomposition of quaternions matrices

MATLAB仿真表明，利用四元数的数学工具简化了球形电机的计算与控制过程，可以使电机按预定轨迹转动，是一种行之有效的方法。

MATLAB simulation shows that the quaternion makes the calculation and control of spherical motor simple , motor rotates along the given trajectory , and it is an efficient method .

1843年，威廉汉密尔顿（williamhamilton）在都柏林发明了四元数，将虚数扩展到四维空间。

Quaternions , which extend imaginary numbers into a further dimension , began to be developed by William Hamilton in Dublin in 1843 .

关于四元数体上重行列式以及Schur公式

On Double Determinant and Schur 's Formulas over Quaternion Field

四元数矩阵的Kronecker积性质

The Approchs to the Properties of the Kronecker Product of Quaternion Matrices

讨论了Hamilton四元数、马氏四元数及其与二维实信号类似的欧拉公式。

In addition , Hamilton quaternion , Ma quaternion and their Euler formula similar to that of two-dimensional real signal were discussed .

并给出两自共轭四元数阵（其一为半正定）的同时GH合同简化形，由此得到两自共轭同时对角化问题的一些结果。

Then simultaneous GH-congruence reduced forms for two self-conjugate matrices and some results about the simultaneous GH-congruence diagonalization of quaternion matrices .

首先给出了阵列接受信号的二维实模型，通过可分离信号和Hilbert变换构造了符合四元数结构的新的信号模型。

A real model of two-dimensional received signal was given and a quaternion signal model through Hilbert transform and separated signal was constructed .

空间6R机器人位置反解的对偶四元数法

Dual Four Element Method for Inverse Kinematics Analysis of Spatial 6R Manipulator