| 用初等变换法判断实二次型的类型 |
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| 引用本文： | 陈利娅,胡劲松. 用初等变换法判断实二次型的类型[J]. 西昌学院学报(自然科学版), 2009, 23(1): 30-32 |
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| 作者姓名： | 陈利娅 胡劲松 |
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| 作者单位： | 西华大学,数学与计算机学院,四川,成都,610039 |
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| 摘 要： | 引入初等合同变换,将实对称矩阵化为对角矩阵,得到实二次型的一个标准形,从而可以用初等合同变换来判断实二次型的类型。同时也给出了正（负）定二次型的一个必要条件和不定二次型的一个充分条件。该方法易于理解,简单实用,计算量小。
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| 关 键 词： | 初等合同变换 实二次型 实对称矩阵 |
Deciding the Type of the Real Quadratic Form by Elementary Congruence Transformation |
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| CHEN Li-y,HU Jin-song. Deciding the Type of the Real Quadratic Form by Elementary Congruence Transformation[J]. Journal of Xichang College, 2009, 23(1): 30-32 |
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| Authors: | CHEN Li-y HU Jin-song |
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| Affiliation: | ( College of Mathematics and Computer Engineering, Xihua University, Chengdu, Siehuan 610039) |
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| Abstract: | By introducing elementary congruence transformation, a symmetric matrix is exchanged to a diagonal matrix and a standard form is obtained. So the type of the real quadratic form can be decided. A necessary condition of the positive （negative） quadratic form and a sufficient condition of the indefinite quadratic form are presented. The method is easy to understand and costs little computation. |
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| Keywords: | Elementary congrnence transformation Real quadratic form Symmetric matrix |
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