| 复正定矩阵的标准性及判定 |
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| 引用本文： | 张慎语,王毅.复正定矩阵的标准性及判定[J].四川理工学院学报(自然科学版),1996(4). |
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| 作者姓名： | 张慎语 王毅 |
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| 作者单位： | 四川联合大学数学系，四川轻化工学院基础部 |
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| 摘 要： | 研究复正定矩阵的性质，提出了矩阵的第二特征多项式和第二特征值的新概念，得到复正定矩阵的＊相合标准形的存在性和唯一性定理；给出由第二特征值计算复正定矩阵＊相合标准形的方法；给出由第二特征多项式判定复正定矩阵的＊相合的方法；给出由低阶矩阵的正定性判定高阶矩阵正定的方法。
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| 关 键 词： | 复正定矩阵 ＊相合 ＊相合标准形 第二特征多项式 第二特征值 |
THE STANDARD FORM AND THE DISCRIMINATION OF COMPLEX POSITIVE DEFINITE MATRIX |
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| Zhang Shenyu.THE STANDARD FORM AND THE DISCRIMINATION OF COMPLEX POSITIVE DEFINITE MATRIX[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,1996(4). |
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| Authors: | Zhang Shenyu |
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| Institution: | Zhang Shenyu (Dept. of Mathematics Sichuan Union University Chengdu 610064 )Wang Yi (Dept. of Basic Courses Sichuan Institute of Light Ind. & Chem. Tech. Zigong 643033 ) |
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| Abstract: | The new concepts of second characteristic polynomial and second characteristic value are proposed in the paper. These are applied to study the unique existence theorem of the standard form of complex positive dofinte matrix. The standard form of complex positive definite matrix is determined by second characteristie values of com plex positive definite matrix. Whether two complex positive definite matrices are conjunctive is completely detrmined by their second charateristic polynomials. Finally, one of the methods of discriminating complex positive definite matrix is discussed by com plex positive definite matrix which has lower order. |
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| Keywords: | complex positive definite matrix conjunctive matrix conjunctive standard form of complex positive definite matrix second characteristic polynomial second characteristic value |
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