Some Research On The Properties Of Nekrasov Matrix And Its Criteria

Nekrasov matrix is a class of special matrix which play an important role in matrix theory. It has numerous applications in many areas such as numerical algebra, electrical system theory, economical mathematics and statistic. Due to its special structure, N ekrasov matrix has many excellent properties and many scolars pay attentions to it. In this paper, we mainly discusses the properties of the diagonally-Schur complement of the N ekrasov matrix and some practical sufficient conditions for generalized N ekrasov matrix. We obtain a series of conclusions which have improved previous results. In this paper, the concrete structure is as follows:In chapter one, we first introduce background knowledge and recent research for results non-singularN ekrasov matrix, and introduce our main works, some basic symbols and definitions.In chapter two, the diagonal-Schur complement of matrix play an very important role to discuss the large complex system. By using the properties of submatrix of Nekraosv matrix and Mathematical inductive method, and employing inequality techniquesin this chapter, we obtain that the diagonally-Schur complement of the N ekrasov matrix relative to its leading principal submatrix is still N ekrasovmatrix.In chapter three, according to the equivalence relation between nonsingular H-matrices and generalized N ekrasov matrix, analyzing the properties of matrix element, constructing relevant positive diagonal matrix factors and combined with inequality techniques, we obtain some new criteria for generalized N ekrasov matrix by constructing the new compression factor and subdividing index set twice.