矩阵半群

From [1], Every transition function is a positive strongly continuous semigroup of contractions on l\, but it isnt a strongly continuous semigroup on l_∞- In fact, the sufficient and necessary condition for a transition function to be a strongly continuous semigroup on l_∞ is that the q—matrix Q is an uniformly bounded q—matrix on l_∞- This is the trivial case.

由Anderson[1]知道转移函数P是l_1空间上正的强连续压缩半群，但P一般来说不是l_∞空间上的强连续半群，而P是l_∞上强连续半群的充要条件是q—矩阵Q是l_∞。

This paper researches linear maps preserving orthogonality,obtains the linear maps preserving othrogonality,it is either a rank -declining or rank -keeping map or a map with nilpotent element in its codomain.

利用分块成向量的方法证明了MnMn(F为域F上所有n×n矩阵构成的乘法半群上的n×n拟正交矩阵组至多含有n个矩阵，利用方程组的解的理论证明了Mn中与给定矩阵A构成两两拟正交矩阵组的矩阵个数不超过n-Rank+1，从而得到Mn上保持拟正交性的线性映射φ要么是降秩的或者保秩的映射，要么φ的值域中含有幂零元。

Calculating the functions of the matrix exponential e has special significance in the theory of linear systems and the theory of semi-groups. Especially, in the modern control theory, no matter the equation is homogeneous or non-homogeneous, the result depends on the calculation of the matrix exponential e.

矩阵指数函数e的计算在线性系统理论及半群理论中有着特殊的作用，在现代控制理论中，无论是齐次方程还是非齐次方程的求解，主要取决于矩阵指数函数e的计算和近似。

In chapter 2, we prove that an abundant semigroup satisfying the regularity is a locally E-solid semigroup if and only if it is an E-local isomorphic image of some abundant Rees matrix semigroup AM over an E-solid abundant semigroup with entries of the sandwich matrix P being regular elements of T.

第二章，我们证明了满足正则性条件的富足半群是局部E-solid(quasi-adequate，R~*-unipotent)半群当且仅当它是某个富足Rees矩阵半群RM的E-local同构像，其中sandwich矩阵的P元素是T中的正则元。

This leads to Rees matrix representation theorems of some generalized completely simple semigroups.

本文首先建立了某类U-半超富足半群的Rees矩阵表示定理，并由此得到了若干广义完全单半群的Rees矩阵表示定理。

Lastly , from a primitive rpp semigroup with zero , we built up a type A blocked Rees matrix semigroup and showed a semigroup S is a primitive rpp semigroup if and only if S is isomorphic toa type A blocked Rees matrix semigroup.

该结果的一个特例就是可消幺半群上的Rees矩阵半群。

By the definition of Green-relation and the analogue of generalized Greens lemma, this paper first studied some properties of H-class、 D--class of rpp semigroups, then by left S-system 、-bisystem and tensor product, we described a blocked Rees matrix semigroup. Especially, the paper studied primitive rpp semigroups .

本文利用在rpp半群上定义的广义Green~(l-关系及相应的广义Green定理，首先研究了rpp半群H~(l-类、D~(l-类的若干基本性质，然后以左S-系、-双系和张量积作为工具，刻画了块Rees矩阵半群结构，最后从带零的本原rpp半群出发，构造出A型块Rees矩阵半群，并证明了一个半群S为本原rpp半群，当且仅当S同构于一个A型块Rees矩阵半群。

Eigenvalue matrix for resolving sparse polynomial equations is constructed by deploying well arranged basis in semigroup algebra k.

本文利用半群代数k中良序基，构造了求稀疏多项式方程组解的特征值矩阵，并给出了可以构造方阵的条件。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

Firstly we introduce the concept of Rees matrix semigroups without zero i.e.

矩形群、左群都是极其重要的半群，在Mario[2]中这两种半群都已有了很好的刻画，本文后两章将给出推广了的矩形群和左群的详细刻画，全文共分三章，具体内容如下：第一章主要对推广之后Rees矩阵半群的刻画进行了描述，在这一章里先介绍了无零Rees矩阵半群的概念，它是一类矩阵半群M=MT；I，？

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。