Criteria For Nonsingular H Matrix

Nonsingular (block) H matrix is an important class of special matrix withextensive applications. It is well known that strictly diagonally dominant ma-trix, diagonally dominant matrix having nonzero elements chain and irreduciblediagonally dominant matrix are the special cases of nonsingular (block) H ma-trix. Considering the importance of such matrix in computational mathematics,mathematical physics and dynamical system theory, to get simple criteria of non-singular (block) H matrix is a heated topic in recent years.In this paper, we ?rstly study the properties of nonsingular (block) H matrix,presenting some new criteria for nonsingular (block) H matrix by constructingpositively diagonal matrix factors. In addition, by using the properties ofα-chains (block) diagonally dominant matrix, applying some inequality techniques,we give some criteria of nonsingular(block) H matrix.In chapter one, we ?rstly present some background knowledge and recentworks for nonsingular (block) H matrix. Then we introduce some basic symbolsand de?nitions used in this paper.In chapter two, by constructing positively diagonal matrix factors and ap-plying inequalities techniques, we give some new criteria for nonsingular blockH matrix. Then we extend these methods to the conditions of block irreduciblematrix and block non-zero chain matrix. Finally, we illustrate the e?ectivenesswith numerical examples.In chapter three, using the properties ofα-chains (block) diagonally domi-nant matrix, applying block matrix technology and the properties of matrix norm,constructing positively diagonal matrix, we get some su?cient conditions for non-singular block H matrix. The superiority of our results is demonstrated by somenumerical examples.