广义严格双对角占优矩阵的三角-Schur补
Triangular Schur Complement of Generalized Strictly Doubly Diagonally Dominant Matrices
摘要: 在研究一类特殊的矩阵时，通常会关注其子矩阵或者其相关矩阵是否具有类似性质。当矩阵A是广义严格双对角占优矩阵时，对广义严格双对角占优矩阵的三角Schur补进行分析。利用严格对角占优矩阵的性质、矩阵无穷范数与谱半径之间的关系，通过不等式的放缩技巧，得到广义养个双对角占优矩阵的三角Schur补是严格对角占优矩阵的结论。
Abstract: When we study a particular matrix, we usually pay attention to whether its submatrix or related matrices have similar properties. When matrix A is a generalized strictly doubly diagonally dominant matrices, the triangular Schur complement of the generalized strictly doubly diagonally dominant matrix is analyzed. By using the properties of strictly dominant matrices, the relation between the infinite norm of matrices and the spectral radius of matrices, the conclusion that the trigonometric Schur complement of generalized strictly doubly diagonally dominant matrices is strictly diagonally dominant matrices is obtained through the expansion and contraction of inequalities.
文章引用：马静. 广义严格双对角占优矩阵的三角-Schur补[J]. 理论数学, 2020, 10(2): 100-105. https://doi.org/10.12677/PM.2020.102016

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