The Criteria Of Specific Shape Inverse M-Matrices

Special matrices play important roles in matrix analysis and matrix computation and have wide applications in computational mathematics, economics, biology, applied mathematics and etc. Inverse M—matrices is one of the most important special matrices. In this paper, by using the properties of inverse M—matrices, and investigating the structure of some kinds of special shape matrices, we get the sufficient and necessary or sufficient conditions of them.In chapter one, we mainly introduce the studied production of the specific shape and type matrix in the near future, and state the research production of inverse M—matrices.In chapter two, partitioning specially and using the properties of schur complements matrices, we get the necessary and sufficient conditions of inverse M—ma trices; the properties of tridiagonal period inverse M-matrices and the sufficient and necessary of the tri-diagonal matrices are associated further, we get the necessary and sufficient condition of the tridiagonal period inverse M—matrices. And we discuss a new class of adding element tri-diagonal period inverse M—matrices that has analogous properties, the necessary and sufficient condition of adding element tri-diagonal period inverse M—Matrices is given, moreover; we give relevant numerical example.In chapter three, based on the chapter one, we defined a new class of adding many elements tri-diagonal period matrices, on the blocked matrices above, integrating the properties of adding element tridiagonal period inverse M—matrices we get a sufficient condition of adding many elements tri-diagonal period inverse M—Matrices, moreover the numerical example is given.In chapter four, using partitioning of block matrix, and associating the properties of five-diagonal inverse M—matrices matrices, we get a sufficient condition of five-diagonal inverse M—matrices, and we prove that the class of five-diagonal inverse M—matrices matrices is closed under Hadamard product.