非负不可约矩阵的广义Perron补矩阵

1989年Meyor为计算马尔可夫链的平稳分布向量构造了一个算法，首次提出非负不可约矩阵的Perron补矩阵的概念，本给出非负不可约矩阵A的广义Perron补矩阵若干性质，并且证明若矩阵A是不可约逆M-矩阵，其广义Perron补矩阵也是不可约逆M-矩阵。     

一类恰含一个3-圈的三色本原有向图指数上界

在传统(单个)非负本原矩阵的基础上,将非负本原矩阵对的研究推广到非负本原矩阵簇,是组合矩阵论中一个崭新的研究内容.事实上,非负矩阵簇可以与多色有向图建立一一对应关系,从而把矩阵的问题转化为图的问题进行研究.该文研究了一类三色本原有向图,它的未着色图中包含n个顶点,一个n-圈、一个(n-1)-圈和一个3-圈,给出本原条件和指数上界.     

非负矩阵谱半径的新界值

非负矩阵谱半径的估计是非负矩阵理论研究的重要组成部分.如果上下界能够表示为非负矩阵元素的易于计算的函数,那么这种估计价值更高.通过构造两个收敛的序列得到非负矩阵谱半径的新界值.数值算例表明其结果比有关结论更加精确.     

关于非负不可约矩阵的广义Perron补的一些性质

1989年Meyer为计算马尔可夫链的平稳分布向量构造了一个算法，首次提出非负不可约矩阵的Perron补的概念。本文给出非负不可约矩阵A的广义Perron补若干性质，并且证明当矩阵A是不可约逆M-矩阵，其广义Perron补也是不可约逆M-矩阵。     

非负矩阵谱半径的新估计

非负矩阵谱半径的估计是非负矩阵理论研究中的重要课题.如果谱半径的上下界能够表示为非负矩阵元素的易于计算的函数,那么这种估计价值更高.通过构造两个收敛的序列得到非负矩阵谱半径的新界值.数值算例表明其结果比有关结论更加精确.     

计算非负不可约矩阵Perron根的对角变换

计算非负矩阵Perron根一般通过矩阵的对角变换,但是有的时候是不可行的．本文为非负不可约矩阵的计算给了一列对角变换．此种变换对所有的非负不可约矩阵实用,并且方便计算,最后给出了数值例子．     

计算非负不可约矩阵Perron根的对角变换(英文)

计算非负矩阵Perron根一般通过矩阵的对角变换,但是有的时候是不可行的.本文为非负不可约矩阵的计算给了一列对角变换.此种变换对所有的非负不可约矩阵实用,并且方便计算,最后给出了数值例子.     

非负矩阵Perron根的下界序列

非负矩阵Perron根的估计是非负矩阵理论研究的重要课题之一.如果其上下界能够表示为非负矩阵元素的易于计算的函数,那么这种估计价值更高.本文结合非负矩阵的迹分两种情况给出Perron根的下界序列,并且给出数值例子加以说明.     

非负广义幂等矩阵

非负幂等矩阵在［１］中已有详细地讨论和重要地应用。［２］给出了Ａ≥０，Ａｋ＋１＝Ａ，ｋ是正整数，Ａｋ是零对称幂等矩阵的充要条件。本文给出了一般非负广义幂等矩阵的充要条件。并讨论了广义幂等矩阵的秩与其广义幂等指数的关系，推广了［２］中的部分结论。     

非负不可约矩阵Perron根的估计

给出了非负不可约矩阵Perron根的一些上下界估计,设A为任意非负不可约矩阵,ρ(A)为其Perron根,则ρ(A)≤max{D_k,(r_1+r_2+…r_k)/k}其中D_k为矩阵A所有k阶主子阵之列和最大值,r_1≥r_2≥…≥r_n为从大到小排序的行和,所得结果易于计算且较经典的Frobienus界值精确.同时也得到一个类似下界.     

非负矩阵Perron根的上下界

1.引言 本文主要讨论非负矩阵,我们将用B≥0和B>0分别表示矩阵B是非负的和正的,也就是B的每一个元素是非负的和B的每一个元素是正的.用p(B)表示方阵B的谱半径,当B≥0时,p(B)也就是B的perron根. 设(n)={1,2,…,n},A=(ai,j)是n×n非负矩阵,我们称     

Row Hadamard majorization on Mm,n

Czechoslovak Mathematical Journal - An m × n matrix R with nonnegative entries is called row stochastic if the sum of entries on every row of R is 1. Let Mm,n be the set of all m × n real...     

Construction of Normal Bimagic Squares of Order 2u

Acta Mathematicae Applicatae Sinica, English Series - An n × n matrix A consisting of nonnegative integers is a general magic square of order n if the sum of elements in each row, column, and...     

Convolution operators on Lebesgue spaces of an n-dimensional cube

This paper is concerned with the problem of diagonally scaling a given nonnegative matrix a to one with prescribed row and column sums. The approach is to represent one of the two scaling matrices as the solution of a variational problem. This leads in a natural way to necessary and sufficient conditions on the zero pattern of a so that such a scaling exists. In addition the convergence of the successive prescribed row and column sum normalizations is established. Certain invariants under diagonal scaling are used to actually compute the desired scaled matrix, and examples are provided. Finally, at the end of the paper, a discussion of infinite systems is presented.     

On infinite doubly substochastic matrices

Summary An infinite matrix is said to be doubly substochastic if it has nonnegative components and each row and each column sum is at most 1. Let x and y be two real sequences which converge to 0 or which are absolutely summable. This paper introduces necessary and sufficient conditions for existence of an infinite doubly substochastic matrix A such that x=Ay concerning partial order and convex hull for sequences.     

Existence of matrices with prescribed Off-diagonal block element sums

Necessary and sufficient conditions are proven for the existence of a square matrix, over an arbitrary field, such that for every principal submatrix the sum of the elements in the row complement of the submatrix is prescribed. The problem is solved in the cases where the positions of the nonzero elements of A are contained in a given set of positions, and where there is no restriction on the positions of the nonzero elements of A. The uniqueness of the solution is studied as well. The results are used to solve the cases where the matrix is required to be symmetric and/or nonnegative entrywise.     

Monotonicity of some perturbations of irreducibly diagonally dominant M-matrices

This paper presents a new result concerning the perturbation theory of M-matrices. We give the proof of a theorem showing that some perturbations of irreducibly diagonally dominant M-matrices are monotone, together with an explicit bound of the norm of the perturbation. One of the assumptions concerning the perturbation matrix is that the sum of the entries of each of its row is nonnegative. The resulting matrix is shown to be monotone, although it may not be diagonally dominant and its off diagonal part may have some positive entries. We give as an application the proof of the second order convergence of an non-centered finite difference scheme applied to an elliptic boundary value problem.     

Generalized fuzzy matrices

We give a systematic development of fuzzy matrix theory. Many of our results generalize to matrices over the two element Boolean algebra, over the nonnegative real numbers, over the nonnegative integers, and over the semirings, and we present these generalizations. Our first main result is that while spaces of fuzzy vectors do not have a unique basis in general they have a unique standard basis, and the cardinality of any two bases are equal. Thus concepts of row and column basis, row and column rank can be defined for fuzzy matrices. Then we study Green's equivalence classes of fuzzy matrices. New we give criteria for a fuzzy matrix to be regular and prove that the row and column rank of any regular fuzzy matrix are equal. Various inverses are also studied. In the next section, we obtain bounds for the index and period of a fuzzy matrix.     

On sharp bounds for spectral radius of nonnegative matrices

We give sharp upper and lower bounds for the spectral radius of a nonnegative matrix with positive row sums using average 3-row sums, compare these bounds with the existing bounds using the average 2-row sums by examples, and apply them to the adjacency matrix and the signless Laplacian matrix of a digraph or a graph.     

7373170279850

We conjecture that 7,373,170,279,850 is the largest integer which cannot be expressed as the sum of four nonnegative integral cubes.