In chapter two, we present some new criterions by choosing the elements of positive diagonally matrix D and using the relations of the matrices A and B (where B = M(A) + M T(A)). At the same time, the judging methods for generalized strictly diagonally dominant matrix with the irreducibility and a chain of nonzero elements are presented.
第二章通过选取正对角矩阵D的对角因子,并利用矩阵A和B的关系得到了几则新的判据(这里B = M(A) + M T(A)),同时也得出了不可约矩阵、具有非零元素链矩阵的相应结论,并说明了其实用性。
Some criterions and properties were presented for a matrix to be a nonsingular H-matrix using matrix's concepts of irreducibility, α-diagonally dominance and α-doubly diagonally dominance and the method of G-function and matrix's directed graph.
In this paper we discuss the block weak irreducibility of partition matrices and nonsinyulary of block weak irreducible diagonally dominant matrices, give corresponding spectral inclusion regions, improve the Brualdi's theorem and corresponding results in  and .
In this paper we consider some beautiful properties of the generalized Perron complement of a nonnegative and irreducible matrix A and it is shown that the generalized Perron complement of a matrix A is still an irreducible inverse M-matrix when A is an irreducible inverse M-matrix.
The concept of the Perron complement of a nonnegative and irreducible matrix was introduced by Meyer in 1989 and was used to construct an algorithm for computing the stationary distribution vector for Markov chain.
An algebraicG-varietyX is called "wonderful", if the following conditions are satisfied:X is (connected) smooth and complete;X containsr irreducible smoothG-invariant divisors having a non void transversal intersection;G has 2r orbits inX.
We find presentations for the irreducible crystallographic complex reflection groupsW whose linear part is not the complexification of a real reflection group.
The finite irreducible linear groups with polynomial ring of invariants
We prove the following result: LetG be a finite irreducible linear group.
For the case of positive characteristic we use the classification of finite irreducible groups generated by pseudoreflections due to Kantor, Wagner, Zalesski? and Sere?kin.
The irreducibility of a subspace U ?= V under the κα implies that, for generic values of the parameter, the braid group Bg acts irreducibly on U.
We use this to disprove a conjecture of Kwon and Lusztig stating the irreducibility of quantum Weyl group actions of Artin's braid group Bn on the zero-weight spaces of all simple Usln-modules for n≥4.
Under the condition of irreducibility, it is show that this is equal to the spectral radius of Jacobi matrix of its generating function.
The question of irreducibility is considered, and a classification of bilinear invariant functionals, intertwining operators, and Hermitian invariant functionals is obtained.
Linear irreducibility of one form of differential equations