quaternion

1. Simultaneous diagonalization of two quaternion normal matrices
   2个四元数正规矩阵的同时对角化问题
2. First, according to the tracking error dynamics and kinematics described by unit quaternion error and angular velocity error, a sliding mode controller is derived based on Lyapunov theory.
   首先根据由误差四元数和误差角速度描述的跟踪误差动力学和运动学方程，设计了基于李亚普诺夫方法的滑模变结构控制律。
3. Since unitary congruence of quaternion matrices is in connection with unitary similarity of quaternion matrices, we also discuss some properties of the unitary similarity of quaternion matrices.
   由于四元数矩阵的酉相合与酉相似有着密切联系，本文还讨论了四元数矩阵的酉相似的一些性质。
4. A kind of control law is designed using unit quaternion and angular velocity by the feedback nonlinearization approach firstly.
   首先利用反馈非线性化方法，给出一种不含非线性扭矩项、仅由四元数和角速度的线性组合构成的控制规律。
5. In addition, the paper also discussed a group of formula of vector differentiation in quaternion form.
   文章还讨论了四元数形式的矢量微分运算的一组计算公式。
6. On Diagonalization of Matrices and Schur Theorem over Quaternion Field;
   四元数体上矩阵的对角化和Schur定理（英文）
7. In this paper, we obtain some inequalities for norm and traces of quaternion matrices.
   本文获得了四元数矩阵的范数和迹的一些不等式，改进了近期的某些结果。
8. The norm of a quaternion is similar to that of a vector. examining resemblances or differences.
   四元数的平均值与矢量的有点相似。检查相似点或不同点。
9. Power Market Reform in European Union and Revelation to China; This paper studies comparatively dual Euler method and quaternion method which are used for the solution of the singularity of the Euler equation.
   欧盟电力市场化改革最新进展及启示对解决欧拉方程奇异性的双欧法和四元数法进行了对比研究。
10. Smooth orientation planner for manipulators based on quaternion and B-spline
    基于四元数和B样条的机械手平滑姿态规划器
11. A license plate location algorithm was presented, which was based on the quaternion specific color-pair edge detection technique.
    提出了一种基于四元数特定颜色对边缘检测的车牌定位算法。
12. Mixed Operation of Quaternion, Special Function Differentiation and Application of Rolle's Theorem in Mizar
    四元数混合运算及特殊函数的微分公式和洛尔定理应用的Mizar实现
13. Simulation Modeling of Satellite Attitude Control System Based on Quaternion Feedback
    基于四元数反馈的卫星姿态控制系统仿真模型建立
14. A New Large-scale Transformation Algorithm of Quaternion to Euler Angle
    一种新的全角度四元数与欧拉角的转换算法
15. The quaternion matrix singular value perturbation theorem is generalized and these results are also new one for complex matrix.
    本文对四元数体上矩阵奇异值摄动定理给出了推广，且这些结果对复矩阵也是新的。
16. Study on Some Matrices Problems over Real Quaternion Division Algebra
    四元数体上代数的若干矩阵问题研究
17. Two kind of linear representations of the generalized quaternion algebras are given, and a necessary and sufficient condition about the isomorphism of two generalized quaternion algebras is obtained.
    给出了广义四元数代数的两种线性表示，导出了两个广义四元数代数同构的充要条件；
18. In the paper the generalized numerical radiuses of real quaternion matrices with symmetric function are defined and theirs inequalities are given.
    本文定义了带有对称函数的实四无数矩阵的广义数值半径并得到了它们所满足的不等式。
19. Inverse Problem for Generalized Toeplitz Matrices over Quaternion Field
    四元数体上广义Toeplitz矩阵反问题
20. After analyzing the relation between a quaternion function and the angular velocity it represents, a smooth angular velocity interpolation algorithm is proposed.
    在分析了四元数函数与角速度的关系后，提出了角速度光滑插值的方法，并能计算出任一时间角速度的值。
21. Discontinuous Characteristic Boundary Value Problems for Hyperbolic Equations in Commutative Quaternion Algebra
    交换四元数代数中一类双曲型方程的间断特征边值
22. Considering the target angle rate changing, an adaptive attitude tracking control law was designed based on the error quaternion, and the corresponding close system stability was also proved.
    考虑目标姿态角速度可以时变的一般情形，设计了基于误差四元数的自适应姿态跟踪控制律，给出了稳定性证明。
23. Calculates the natural logarithm of a quaternion.
    计算四元数的自然对数。
24. In the paper a general space-time transformation theory is established with complex quaternion as space-time algebra.
    以复四元数为时空代数，建立了一个广义时空变换理论。
25. Custom inspector that shows the X, Y, Z, W quaternion components of a transform.
    创建一个自定义检视面板，显示变换的X，Y，Z，W四元数组件。
26. Extracting Dynamic Error of Accelerometer Tested on Three-axis Turntable by Quaternion
    用四元数法提取加速度计三轴转台测试中的动态误差量
27. So, dual Euler method is better than quaternion method in the solution of the singularity of the Euler equation.
    对解决欧拉方程奇异性的双欧法和四元数法进行了对比研究。
28. The original color image was first represented by using quaternion Same-Hue-Full-Saturation ( SHFS) form.
    首先将输入彩色图像用同色调全饱和度四元数形式表示；
29. Arithmetic distance and distance of skew-Hermitian matrices over quaternion division ring with an involution
    具有对合的四元素体上斜Hermitian矩阵的距离与算术距离
30. The main purpose of this paper is to study a new proof of extended unitary diagonalizable of self-conjugate matrix in quaternion field and deduce other properties concerned.
    探讨了四元数体上自共轭矩阵的广义酉对角化的新证法，并由此推出其它相应的性质。

noun

1. the cardinal number that is the sum of three and one

   Synonym:    four4IVtetradquaternquaternaryquaternityquartetquadrupletfoursomeLittle Joe