四元数

A new effective method which makes use of quaternion theory is presented to implement location transformation of a plane curve.

利用实四元数理论，提出了一种将一般位置平面曲线变换到空间任意指定位置的一种简捷方法。

Those new methods are based on Jacobsons theory and its characteristic structure which make the problem equivalent to a 2 x 2 matrix polynomial equation with diagonalizable solutions.

1新方法及其比较主要介绍了求解四元数多项式方程的两种传统方法和两种新的方法，并在分析过程中进行了对比。

Zeros of linear polynomials with real efficients are the real solutions of the original polynomial equation.

5四元数二次方程的显式解：利用改进的新方法完全可以得到二次方程解的显式表示以及关于解的具体情况的一些充分必要条件。

But the space is the matter, the matter is the string vibration, only has from this the time which vibrates f=1/T to draw out only then has the physics significance, therefore T is in the true significance time, from this deduction: What imaginary number Ict expresses is void, may write *ct,=I pure imaginary number, also is it with Number space Sigma (x1i*x2j)(i, j is subscript, i=j=1,2,3) differs 90 in the space, the shape for example: Psi ==a+Ib, constitutes a duplicate space by psi i* psi j,(definition mark * for ordinary multiplication) may use Four single numbers

而空间就是物质，物质就是弦的振动，只有从这个振动f=1/T引出的时间才有物理意义，所以T才是真正意义上的时间，由此推论：虚数Ict所表达的是一个虚空间，可以写成*ct，=I纯虚数，也即它与实空间Σ(x1i*x2j)(i，j为下标，i=j=1，2，3)在空间上相差90度，形如：ψ==a+Ib，由ψi*ψj构成一个复空间，可用四元数

It is studied factorizing a matrix over quaternion field to the product of two self-conjugate matrices. And some useful results are obtained.

摘要研究了四元数矩阵分解为两个自共轭矩阵乘积，其中有一个是非奇异阵的条件，得到了一些有用的结果。

Quaternion field; matrix equation; structure-preserving algorithm; iterative method

四元数体；矩阵方程；保结构运算；迭代算法

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。

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

在这方面，四元数的理论和方法或许是合适的。

Through it, we can get quaternion some characteristics.

通过它，可以掌握四元数的一些特征。

To answer that, you first need to calculate the norm of your quaternion.

答案在这，你首先需要计算你的四元数的平均值。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。