基于AFS逻辑的模糊聚类分析

应用 AFS结构[8] 和 EI代数 [8] 给出一个新的模糊聚类分析方法。它和人类根据某些模糊特征对一些对象进行聚类分析的过程类似。并通过例子说明该方法分类的结果与用直觉分类的结果相似。     

A simple technique for selection of complementary chromatographic methods by correlation of data

Summary A simple graphic method using matrix diagrams has been developed to facilitate the most efficient use of data from chromatographic systems. A quantification of this data gives a value that relates chromatographic systems with random distributions. Uncorrelated or weakly correlated systems yield the best results.     

几类矩问题的矩阵解法

本文利用矩阵论的方法对讨论截断矩问题,无穷矩问题以及[带不等号的矩问题。     

Sums and Products of Square-Zero Matrices

We show that for any two n × n square-zero matrices A and B over a division ring, if the right column spaces of AB and BA are the same, then the rank of AB is at most n/4, and if, in addition, the right null spaces of AB and BA are the same, then the rank of A + B is at most n/2. This generalizes some known results.     

Nonnegative Rank Factorization of a Nonnegative Matrix A with A A ≥0

In this article we obtain a nonnegative rank factorization of nonnegative matrices A satisfying one or both of the following conditions: (i) AA † ≥0 (ii) A † A ≥0, thus providing a new set of conditions that guarantee the existence of a nonnegative least-squares solution of a linear system. Indeed, the characterization of such matrices improves some of the previous known conditions for the existence of a nonnegative least-squares solution of a linear system.     

On the inverse of a general tridiagonal matrix

In the current paper a new efficient computational algorithm to find the inverse of a general tridiagonal matrix is presented. The algorithm is suited for implementation using computer algebra systems such as MAPLE, MATHEMATICA, MATLAB and MACSYMA. Symbolic and numeric examples are given.     

Homogeneous Nilpotent Matrices in Two Variables

We give a general geometrical procedure to construct nilpotent morphisms Φ : F → F(d), with F a vector bundle on ?¹, obtaining an analog of the Jordan canonical form. We investigate the possible splitting types of F in dependence on the degeneration behavior of Φ. Applications to nilpotent matrices with an arbitrary number of variables are also given.     

Nonnegative Rank Factorization of a Nonnegative Matrix A with A A ≥0

In this article we obtain a nonnegative rank factorization of nonnegative matrices A satisfying one or both of the following conditions: (i) AA ? ? 0 (ii) A ? A ? 0, thus providing a new set of conditions that guarantee the existence of a nonnegative least-squares solution of a linear system. Indeed, the characterization of such matrices improves some of the previous known conditions for the existence of a nonnegative least-squares solution of a linear system.     

On some characterisations of totally unimodular matrices

A characterisation of totally unimodular matrices is derived from a result of Hoffman and Kruskal. It is similar in spirit to a result of Baum and Trotter. Its relation with some other known characterisations is discussed and in the particular case where the matrices have (0, 1) entries, we derive some properties of the associated unimodular hypergraphs. Similar results for balanced and perfect matrices are also reviewed.