四元数

Quaternion matrix, singular value decomposition, CS decomposition,canonical angle.

由于四元数矩阵乘法运算的复杂性，利用【n，12}的方法很难求出具体的奇异值分解式来。

The author generalized the results of the centralizer of matrix over complex number field to Real Quaternion field .

推广了数域上的矩阵中心化子理论，得到了实四元数体矩阵上的中心化子理论

This paper proposes a flexible and reliable camera calibration of stereo vision measurement system based on unit quaternions with optical reference bar, which has three small collinear infrared LED feature points and the lengths between these feature points have been precisely calibrated.

提出了一种利用光学参考棒，基于单位四元数法的灵活、有效的立体视觉测量系统现场校准技术。

Keep in mind that, as is the case with matrices, quaternion multiplication is not commutative!

紧记，矩阵在此种情况下，四元数的乘法是不可进行交换的。

A 2D harmonic model based on the quaternion was constructed,and a special four-order cumulant was defined.

构造了合适的基于四元数的二维谐波模型，根据此模型定义了特殊的四阶累积量切片，分析了加性高斯在有色噪声中的二维三次非线性相位耦合。

The quaternion signal model was constructed through the separated signal and its Hilbert transform. The corresponding four order cumulant was defined to restrain the additive Gauss noise and the frequency was extracted using the properties of Hamilton quaternion and hypercomplex.

并根据该模型利用特殊的四阶累积量切片分析了加性高斯有色噪声中二维谐波频率估计及联合Hamilton四元数和超复数在二维谐波频率估计中的应用前景。

Based on a brief review on developments of number system, a new developed pattern is proposed. The quaternion is extended to a matrix form aI+bA+cB+dC, in which the identity matrix I and three special matrices A, B, C correspond to number 1 and three units of imaginary number i, j, k, respectively.

在数系发展的基础上，提出了一种新的发展模式：四元数推广为矩阵形式aI+bA+cB+dC，其中单位矩阵I和3个特殊矩阵A，B，C分别相应于数1和虚数单位i，j，k。

In the last of this dissertation, we give necessary and sufficient conditions for the existence of and the expressions of perpositive semidefinite solutions and bipositive semidefinite solutions to some systems of quaternion matrix equations.

给出了某些四元数矩阵方程组有广亚半正定解，双半正定解的充要条件及其表达公式；研究了矩阵方程组的最小二乘解，极小范数的最小二乘解，在某些约束条件下的最小二乘解和极小范数的最小二乘解，给出了其有这些解的充要条件及其表达公式。

It contains 1029 leaves of strong, smooth vellum, fresh-looking today, despite their great antiquity, arranged in quires of four sheets, or quaternions.

它载有1029叶强，顺利vellum ，新鲜前瞻性今天，尽管他们的伟大，古物，安排在quires四个床单，或四元数。

Quaternions extend the concept of rotation in three dimensions to rotation in four dimensions.

四元数将三维中旋转的概念扩展到四维中的旋转。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。