| 欧氏空间上的正定变换和半正定变换 |
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| 引用本文： | 杨闻起.欧氏空间上的正定变换和半正定变换[J].西北纺织工学院学报,2012(2):251-253. |
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| 作者姓名： | 杨闻起 |
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| 作者单位： | 宝鸡文理学院数学系,陕西宝鸡721013 |
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| 摘 要： | 引入了欧氏空间上的正定变换和半正定变换的概念,建立了与正定矩阵和半正定矩阵紧密联系的两类线性变换.说明了在标准正交基下正定变换（半正定变换）与正定矩阵（半正定矩阵）的关系,给出了它们的等价刻画,并得到了它们的其他性质.
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| 关 键 词： | 对称变换 对称矩阵 正定变换 正定矩阵 |
On positive definite transformation and positive semi-definite transformation on the Euclidean |
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| YANG Wen-qi.On positive definite transformation and positive semi-definite transformation on the Euclidean[J].Journal of Northwest Institute of Textile Science and Technology,2012(2):251-253. |
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| Authors: | YANG Wen-qi |
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| Affiliation: | YANG Wen-qi(Department of Mathematics,Baoji University of Arts and Sciences,Baoji,Shaanxi 721013,China) |
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| Abstract: | To further study the relationship between linear transformations and matrices,the positive definite transformation and positive semi-definite transformation are introduced.The relation between the positive（semi-） definite transformation and the positive（semi-） definite matrix are given.The equivalence conditions and some properties of the positive definite transformation and positive semi-definite transformation are discussed. |
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| Keywords: | symmetric matrix symmetric transformation positive definite transformation positive definite matrix |
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