| 关于和与积相等的矩阵对 |
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| 引用本文： | 邵逸民. 关于和与积相等的矩阵对[J]. 浙江大学学报(理学版), 2009, 36(6): 609-612. DOI: 10.3785/j.issn.1008-9497.2009.06.001 |
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| 作者姓名： | 邵逸民 |
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| 作者单位： | 苏州市职业大学,教育与人文科学系,江苏,苏州,215104 |
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| 摘 要： | 和与积相等的矩阵对之间有着密切的联系．从矩阵的秩、非奇异性、特征值、对角化、正定性等方面，讨论了这对矩阵的一些性质．最后，作为应用，导出了几个新的关于正定矩阵的Kantorovich型矩阵不等式．
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| 关 键 词： | 秩 特征值 对角化 矩阵不等式 |
On matrix pair (A,B) with the condition A+B=AB |
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| SHAO Yi-min. On matrix pair (A,B) with the condition A+B=AB[J]. Journal of Zhejiang University(Sciences Edition), 2009, 36(6): 609-612. DOI: 10.3785/j.issn.1008-9497.2009.06.001 |
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| Authors: | SHAO Yi-min |
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| Affiliation: | SHAO Yi-min (Department of Education and Humanities, Suzhou Vocational University, Suzhou 215104, Jiangsu Province, China) |
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| Abstract: | If matrix pair (A,B) satisfies the condition A+B=AB,these two matrices have some connections.Some properties are presented,which are concerned with the rank,invertibility,eigenvalues,diagonalization and positive definite property of these two matrices.As an application of the obtained results,some new Kantorovich-type inequalities for the positive definite matrix are also derived in the end. |
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| Keywords: | rank eigenvalue diagonalizable matrix inequalities |
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