The New Matrix Is ​​diagonally Dominant Form And M-matrix And The H Matrix

M-matrices and H matrices are important matrix species of the research for numeric algebra -the important branch of computational mathematics. The research for M-matrices and H matrices has too much pivotal action in computational mathematics and the other lots of applied scopes. In this paper, we put emphasis on introducing the concept, determinant and equivalent typicality of the two important matrix species. We provide some new concept of generalized diagonally dominant matrices to research M- matrices and H matrices. And we obtain some practical brief determinant for M-matrices and H matrices. The results don't request that the matrices must be predetermined diagonally dominant, and non-diagonally dominant rows can get n-I. It's adapted to far-ranging matrix species. In this paper, four chapters are included: In chapter 1, some basic concepts about matrix theory using in this dissertation are introduced; In chapter 2, the definitions of irreducibility conjugacy diagonally dominant matrix and conjugacy diagonally dominant matrix with nonzero element chain is provided, and we obtain two subclasses of H matrices; In chapter 3, a new concept of diagonally dominant matrix art double a diagonally dominant matrix is provided, and we obtain new practical brief determinant for M-matrices and H matrices through the research for part double a diagonally dominant matrix. This determinant only need brief algebra connecting expression, and don't request that the matrices must bepredetermined diagonally dominant, and non-diagonally dominant rows canget n- l. It's adapted to ttrr-ranging matrix species.ln chapter 4, a new concept of diagonally dominant matrix-weightedconnective diagonally dominant matrix is provided, and we obtain new briefsufficient and need conditions of M-matrices through the research fOr weightedconnective diagonally dominant matrix.