偶数阶张量core逆的性质和应用

张量广义逆是张量理论研究的重要内容之一,在近年张量广义逆研究的基础上.该文给出在爱因斯坦积下张量core逆的性质、张量偏序和张量方程A*X=B在条件χ∈R(A)下的最小二乘解等.

A New Class of Partial Orders

Let R be a unital*-ring.For any a,w,b∈R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b∈R are w-core invertible.We say that a is below b under the w-core partial order if a_(w)^(#)a=a_(w)^(#)b and a_(w)a_(w)^(#)=bwa_(w)^(#),where a_(w)^(#)denotes the w-core inverse of a.Characterizations of the w-core partial order are given,and its relationships with several types of partial orders are also considered.In particular,we show that the core partial order coincides with the a-core partial order,and the star partial order coincides with the a*-core partial order.

关于矩阵的Sharp序、*序和减序

给出矩阵Sharp序的一个新的刻画,由此得到(半)正定矩阵Sharp序与其平方矩阵Sharp序之间的关系.我们还讨论正规矩阵的*序与减序之间的关系,推广了关于Hermmice矩阵的相应结果.

The L^(*) Partial Order on the Set of Group Matrices

In this paper,we use the Lowner partial order and the star partial order to introduce a new partial order(denoted by"L^(*)")on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L*partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.

矩阵核心逆偏序的研究

研究了矩阵的核心逆偏序,然后给出了核心逆偏序的若干性质及等价条件,得到了两个矩阵乘积反序律成立的条件,并进一步讨论了扰动后的核心逆偏序.

基于粗糙集理论偏序决策表知识获取方法研究

介绍了基于偏序关系的偏序决策表,研究了偏序决策表各条件分类和决策分类集合之间的关系,提出了从各分类中计算偏序决策表核及属性约简方法,通过实例,验证了这些方法的有效性。

B(H)上的核偏序与对偶核偏序

设H是无限维复Hilbert空间,B(H)是H上全体有界线性算子构成的代数,先给出核偏序和对偶核偏序的性质,然后运用算子分块矩阵方法研究核偏序、对偶核偏序与减偏序的关系,并进一步给出两个算子A,B核偏序下确界A∧B的表示.

核逆和核偏序的刻画

研究矩阵核逆的相关性质和基于核逆的核偏序的等价刻画。通过对Pauli矩阵的矩阵类型、数值刻画、代数关系等的研究,得出Pauli矩阵的性质。利用Pauli矩阵的性质,推得Pauli矩阵在量子信息中的应用,如密度矩阵的Bloch表示、Pauli矩阵的函数、Tsirelson不等式和密度矩阵的常用度量表示。