| 对角占优矩阵非奇异的充分必要条件 |
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| 引用本文： | 张成毅.对角占优矩阵非奇异的充分必要条件[J].西北纺织工学院学报,2012(1):112-116. |
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| 作者姓名： | 张成毅 |
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| 作者单位： | 西安工程大学理学院,陕西西安710048 |
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| 基金项目： | 陕西省教育厅专项科研基金资助项目（2011JK0492）;中国博士后基金项目（18420041）;西安工程大学科学研究基金项目（BS1104） |
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| 摘 要： | 提出了对角均势矩阵的定义，并通过分析对角占优矩阵的内部结构，发现对角占优矩阵是否具有对角均势主子阵是影响该类矩阵非奇异的根本原因．在此基础上，给出了该类矩阵非奇异的几个充分必要条件．
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| 关 键 词： | 对角占优矩阵 对角均势矩阵 非奇异 |
On sufficient and necessary conditions of nonsingularity of diagonally dominant matrices |
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| ZHANG Cheng-yi.On sufficient and necessary conditions of nonsingularity of diagonally dominant matrices[J].Journal of Northwest Institute of Textile Science and Technology,2012(1):112-116. |
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| Authors: | ZHANG Cheng-yi |
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| Affiliation: | ZHANG Cheng-yi ( School of Science, Xi＇ an Polytechnic University, Xi＇an 710048, China) |
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| Abstract: | The definition of diagonally equipollent matrix is proposed firstly, and by studying the structure of the diagonally dominant matrix what causes that a diagonally dominant matrix is nonsingular is found that it is wheth- er this matrix has a diagonally equipollent principal submatrix or not. On the basis of the findings, several suffi- cient and necessary conditions of which a diagonally dominant matrix is nonsingular are raven. |
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| Keywords: | diagonally dominant matrix diagonally equipollent matrix nonsingular |
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