查询词典 ring of matrices

The first part of the book is concerned with rings and modules, matrices over a ring, affine geometry and projective geometry over a Bezout domain.

内容包括：基本概念，群表示的特徵标，点群的表示，群代数与对称群的表示，有限群的实表示与复表示，有限群表示在群论中某些应用和有限群的模表示等。

Let R be an arbitrary commutative ring with identity, gl the general linear lie algebra over R consisting of all n × n matricesover R and with the bracket operation = xy -yx, t the lie subalgebraof gl consisting of all n×n upper triangular (resp., strictly upper triangular ) matrices over R and d the lie subalgebra of gl consisting of all n×n diagonal matrices over R.

在第三章中，对R是交换环的情形，讨论了典型李代数的导子代数的结构问题：设R是一个含幺交换环，gl是R上一般线性李代数。t是gl的所有n阶上三角矩阵(相应地，严格上三角矩阵)构成的子代数，d是gl的所有n阶对角阵构成的李代数。

As an application, we also describe the Jordan automorphisms of the algebra of upper triangular matrices over commutative rings, and give a sufficient and necessary condition for a commutative ring being connected.

作为应用，我们还刻划了交换环上的上三角矩阵代数的Jordan自同构，并给出了一个交换环是连通环的充要条件。

A simultaneous decomposition theorem of a matrix triplet over an arbitrary division ring F and its practical algorithm are derived based on complicated techniques of matrices.

我们导出了任意除环上三矩阵的同时分解定理，给出了其具体的算法。

In this paper, by using the residue class ring of polynomial ring and the diagonalization of matrixa a fast algorithm for the inverse of r _circular matrices is derived.

本文从多项式环的剩余类环出发，利用相似矩阵的对角化，设计了r-循环矩阵求逆的快速算

Geometry of matrices;;division ring;;block triangular matrices;;maximal sets of rank;;arithmetic distance;;adjacency preserving

论文导师黄礼平，论文学位硕士，论文专业应用数学论文单位长沙理工大学，点击次数 3，论文页数 41页File Size1325K

The weighted Moore-Penrose inverse is a special generalized inverse which is an important basic tool in many branches of mathematics and has extensive applications in other fields such as economics, information processing, automatic control, etc. Recently, the study of generalized inverse of matrices associating with more general algebra such as ring, semiring and so on generalize the theory and methods of generalized inverse deeply and characterize the structure of algebra as well.

加权Moore-Penrose逆是一种特殊的广义逆，它不仅是许多数学分支的基本工具，而且在经济学、信息处理、自动控制等其他领域有着广泛的应用，近年来，结合环、半环等更一般的代数系统的矩阵广义逆的研究，不仅将广义逆的理论和方法作了更加深入的推广，而且也成了刻画代数结构的有力工具。

They form usually a ring, but some fields may be composed of three matrices aI+bA, aI+cB, aI+dC, and of some special 2-order, even n-order matrices. It is a new type of hypercomplex number fields.

它们一般组成环，但3种矩阵aI+bA，aI+cB，aI+dC及某些特殊的二阶甚至高阶矩阵可以组成域，这是一类新的超复数系。

Some striking examples of this are the group of invertible linear maps or matrices, and the ring of linear maps of a vector space.

在这里，一个向量是一个有方向的线段，由长度和方向同时表征。

Then, making use of the concept of eigenstate of polarization , the Jone's matrices of the coupler and the fiber are discussed in order to study the polarization state of the light in the resonator ring. The situation can be distributed into three kinds, two ESOPs are orthogonal, not orthogonal and only one ESOP exits, and each coincides to the special quality of the components in the ring.

其次借助偏振特征状态概念对偏振环中的光束偏振状态进行研究，从耦合器和光纤的琼斯矩阵着手，推导出表达偏振特性的公式，再将偏振情况分为三类，分别是两ESOP正交、不正交和只有一个ESOP，每一种情况都与组成光纤环的元件实际的性能相符。

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。