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1·The concept of local double diagonally matrix is introduced in this paper, and three sufficient conditions of the generalized sub-diagonally dominant matrices are obtained.

提出局部次对角占优矩阵的概念，得到了广义次对角占优矩阵的二个充分条件。

2·This article introduces the concept of local diagonally dominant matrics, studies the properties and eigenvalues of the matrics and offers its application in stability theory.

引进了弱局部对角占优阵的概念，研究这类矩阵的性质及其特征值问题，并给出了在稳定性理论中的应用。

3·The estimation on the inverse elements of strictly diagonally dominant tridiagonal matrix is established; in this estimation, the nonnegative condition of matrix elements is moved.

利用严格对角占优和三对角矩阵的某些特性，推导出严格对角占优三对角矩阵逆元素的统一估计式。

4·Generalized strictly diagonally dominant matrices play an important role in many fields, but it isn't easy to determine a matrix is a generalized strictly diagonally matrix or not.

广义严格对角占优矩阵在许多领域中具有重要作用，但其判定是不容易的。

5·In this paper we propose the concept of a weak strictly diagonally dominant matrix given some DE terminate sufficient conditions for generalized strictly diagonally dominant matrices.

本文提出了弱严格对角占优矩阵的概念，并由此给出了广义严格对角占优矩阵的若干判定条件。

6·In this paper, we give the estimates for the upper and lower bounds on the inverse elements of strictly diagonally dominant periodic tridiagonal matrices, and improve the latest findings.

本文给出了严格对角占优周期三对角矩阵逆元素上界和下界的估计，改进了一些学者近期的研究结果。

7·The calculation methods of diagonally dominant matrix in-situ replacement are researched, including the matrix determinant, the matrix equation unknown and the matrix inversion computation.

研究对角占优矩阵原位替换解算方法，包括矩阵行列式、矩阵方程未知数和矩阵逆阵的解算。

8·Based on the properties of block diagonally dominant matrices, generalized strictly diagonally dominant matrices and nonsingular M-matrices. We give the new condition of nonsingular matrices.

利用矩阵的块对角占优、广义严格对角占优以及非奇异m -矩阵的性质及理论，给出了矩阵非奇异的判定条件，拓展了矩阵非奇异性的判定准则。

9·In this paper, some sufficient conditions and a necessary condition for a matrix to be a generalized strictly diagonally dominant matrix is given. Some previous results are improved and generalized.

本文给出了广义严格对角占优矩阵的若干充分条件和必要条件，从而改进和推广了一些已有的结果。