Judgement For Nonsingular H-matrices And Estimation For The Eigenvalues Of Matrices

Non-singular H -matrix is a kind of very important and special matrix, it has a broad applications in the calculation of mathematics, mathematical physics, control theory, economic mathematics, Matrix theory, neural network large-scale systems, stability research of linear time-delay system, and so on, but the actual determination a matrix is a non-singular H -matrix is very difficult. This paper presents gives several new practical delay-independent conditions to nonsingular H -matrix, These conditions expanded the scope of judgementing nonsingular matrices, a numerical example is given to show determination range of more extensive.Estimation for the eigenvalues of matrices has been a very hot topic in the matrix analysis field, they play an important role in many application field. We know that localization and distribution of eigenvalues is given the size of the matrix eigenvalue in the complex plane, that is, a range is given in their respective regions.In many branches of natural science, there are not needed to accurately calculate the eigenvalue of matrices, and only give a general distribution.This dissertation analysis the above two points from some aspects, The main results and innovations are as follows:1. By constructing a positive diagonal matrix, the traditional algebraic inequality applied to the positive diagonal matrix structure, and thereby giving judge rules.2. Using the theorys of disk theorem, given estimation for the eigenvalues of matrices,so as to solve the problem of estimation for the eigenvalues of matrices, obtained some better results3.In order to increase in convincing, the used matrix what are the validity and sophistication has universality and general.4. The obtained results do not have pre-diagonally dominant and non-diagonally dominant row to n-1 line, in order to a wide range of matrices.