| 摘要: |
| 矩阵被广泛应用于数学物理、控制论、电力系统理论等领域，关于非奇异〖WTHX〗M〖WTBZ〗〖KG-*2〗-〖KG-*6〗矩阵最小特征值的估计成为研究的热点；利用相似变换不改变矩阵特征值给出不可约非奇异〖WTHX〗M〖WTBZ〗〖KG-*2〗-〖KG-*6〗矩阵最小特征值的上下界；该方法所得估计结果仅依赖于〖WTHX〗M〖WTBZ〗〖KG-*2〗-〖KG-*6〗矩阵的元素，易于计算；最后通过数值算例表明新估计式在一定条件改进了现有的相关结果. |
| 关键词: 上下界 不可约 M-矩阵 最小特征值 |
| DOI： |
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| Upper and Lower Bounds for the Minimum Eigenvalue of Irreducible M matrix |
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ZHONG Qin
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| Abstract: |
| M matrix is widely used in mathematical physics， cybernetics， electric system and so on. In recent years， the bound estimates for the minimum eigenvalue of nonsingular M matrix have become an important topic. The upper and lower bounds for the minimum eigenvalue of irreducible nonsingular M matrix are given according to that the similar transform does not change the eigenvalue of a matrix. The estimating formula are easier to calculate since the estimated results only depend on the entries of M matrix. Numerical example illustrates that the new inequalities improve the existing related results. |
| Key words: upper and lower bounds irreducible M matrix minimum eigenvalue |
