行列式的

Using matrix characteristic value to solve determinant question.

利用矩阵的特征值解决行列式的问题。

There are many methods to compute determinant, but the different methods, in the actual computation process, only suit for the different characteristic determinant. The present paper mainly studies 14 kinds the most common and also the most important methods.

计算行列式的方法非常的多，在实际的计算过程中不同的方法往往适合于不同特征的行列式，本论文主要研究其中的十四种最常用的也是最重要的方法。

The second part is the computational methods of the determinant: This part is core part in the full text, and mainly studied 14 kinds computational methods which nearly covered each kind of the characteristic of the determinant computation, including the definition method, the triangle method, Canada method and so on.

第二部分为行列式的计算方法：这一部分是全文的核心部分，主要研究了几乎覆盖各种特征的行列式计算的十四种重要方法，包括定义法、三角形法、加边法等，它们为我们计算行列式提供了方便快捷的途径。

Some basic properties of σ- LFSR over F4 are studied, such as nonlinearity, cycle structure distribution of state graph, the largest period and counting problem related. The conclusions are as follows:The coefficient ring of σ-LFSR is isomorphic to the matrix ring over F,. The cycle structure of σ- LFSR is consistent with that of the determinant of the corresponding polynomial matrix if and only if the feedback polynomial of - LFSR does not contain nontrivial factor over F2,. The counting formula of the number of σ- LFSR with inconsistent cycle structure is also showed in that part. The period of σ-LFSR with degree n is maximum if and only if the determinant of the corresponding polynomial matrix is the primitive polynomial with order 2n over F2,.

本文研究了有限域F_4上的σ-LFSR的一些基本性质，如非奇异性、状态图的圈结构的分布、最大圈的充要条件及相关的计数问题等，得到以下结论：σ-LFSR的系数环同构于F_2上的矩阵环；σ-LFSR的状态图的圈结构与对应的多项式矩阵的行列式的圈结构一致的充要条件为σ-LFSR的反馈多项式不含有非平凡的F_2上的因式，给出了圈结构不一致的σ-LFSR的计数公式； n次σ-LFSR周期达到最大，当且仅当对应多项式矩阵的行列式为F_2上的2n次本原多项式。

When the actuated joint was rotary actuation, kinematic Jacobian matrix of the manipulator was a diagonal matrix. So it was an uncoupled mechanism. As the actuated joint was linear one, Jacobian matrix of the manipulator was an identity 3×3 matrix and its determinant was equal to one. Manipulator, therefore, was singularity-free fully-isotropic throughout the entire workspace.

当以转动输入为主驱动时，运动雅可比矩阵为3×3阶对角阵，故机构为无耦合并联机构；当以移动为主驱动时，雅可比矩阵为3×3阶单位阵，且其行列式的值为1，所以在整个工作空间内机构表现为无奇异完全各向同性。

We should distinguish the square bracket from two straight bars enclosing a determinant.

我们应将方括号与用以围住行列式的两条直线区别开。

The element permutations and values of the Vandermonde determinant have highly symmetry, which makes the determinant applied widely in mathematics.

Vandermonde行列式的元素排列和行列式的值都具有高度对称性，是一个具有广泛应用的行列式。

First,the determinant is regarded as a function of or- der n and denoted by D;Second,the determinant is expanded by row or by column,then the relation in both of Dand subdeterminants will be examined in details to set up certain a recursion,generally speaking,it must be a homogenous or a non homogenous recursion;fi- nally the coefficients of the general solution are found out with the aid.

给出了用递归关系方法求任意 n 阶行列式的值的一般方法：首先，把已知的 n 阶行列式看作为阶数 n 的一个函数，记为 D；其次，按行或按列展开这个行列式，并仔细观察存在于余子式及 D里的关系，建立关于 D的某一递归关系，此关系总为一个齐次的或非齐次的递归关系；最后，借助于 D(0)、D(1)和D(2)等求出递归关系的通解的系数。

When any two rows or two columns are interchanged, the sign of the determinant is changed.

当任何两行或两列互换时，行列式的正负号改变。

This determinant is a special case of the resultant of two polynomials.

这个行列式是两个行列式的结式的特殊情形。

The physiology of the skin machine body for the sake of the environment in the maintenance stability, but eject a body metabolism creation of metabolism thing BE'grease', summer perspire many various skin disease light or good, autumn perspire little metabolism thing metabolism don't go out, various skin disease made, this be the skin machine body of various burning disease.

皮肤机体的生理为了维持内环境稳定，而排出身体代谢产生的代谢物是'油泥'，夏天出汗多各种皮肤病就轻或好了，秋天出汗少代谢物代谢不出去，各种皮肤病就犯了，这就是皮肤机体的各种炎症。

If I had anything tender in me, I shot it dead.

如果我有什么招标的话，我枪死亡。