矩阵代数

Letbe Ra PID. M_n the n×n full matrix algebra over R,and f denotethe linear bijection over M_n.

设R是主理想整环，M_n是尺上全矩阵代数，f为M_n上的可逆线性算子。

It might be a better way to view the multivariate analysis as one in a multi-dimensions vector space because characteristic roots and characteristic vectors are related in that way.

因为各方面的原因，包括时间上及数学基出方面的原因，现在不太可能从头到尾细致地学一遍空间解释几何及矩阵代数，以及关注太多的多元统计上的细节，我只求会用。

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。

We prove that the Jordan semi-triple derivable maps of the algebra of all n×n matrices over a 2-torsion free commutative ring with unity is the sum of an inner derivation and A_φ, where A_φis the image of A underφapplied entrywise andφis an additive derivation over R.

证明了作用在一个包含单位元的可交换的2-无挠环上的矩阵代数上的拟三重Jordan可导映射是一个内导子与A_φ的和(这里A_φ是A在φ下逐点作用的像)。

In chapter 3 we first characterize the Jordan semi-triple derivable maps of matrix algebras.

第三章主要对矩阵代数上的拟三重Jordan可导映射进行了刻画。

Chapter 6 contains the matrix algebra used in this class.

课堂中所将提到的矩阵代数及相关理论皆可参考这本书的第6章。

There is background material on study design, bivariate regression, and matrix algebra.

有背景材料的研究设计，二元回归，和矩阵代数。

Both Hurwitz stability and Schur stability of families of matrices are addressed using the matrix algebra method.

应用矩阵代数方法研究矩阵族的稳定性（包括Hurwitz稳定性和Schur稳定性）。

It is not easy to solve the problem of tensor product multilinear mapping if only matrix algebra knowledge is used. The introduction of structure matrix will make this problem much easier to be solved and more acceptable among people.

在解决张量积多重线性映射问题时，只用矩阵代数知识解决问题有些繁琐，而引入结构矩阵来解决张量积多重线性映射问题，不仅能使问题变得更加简单而且更加容易理解接受。

The automorphisms of matrix algebras and their subalgebras are one of important subject in matrix theory.

矩阵代数及其子代数的自同构是矩阵理论研究领域中的一个非常活跃和成果丰硕的课题。

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。