| 二次型性质的若干应用 |
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| 引用本文： | 薛蓉华.二次型性质的若干应用[J].福建工程学院学报,2011,9(3):273-275. |
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| 作者姓名： | 薛蓉华 |
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| 作者单位： | 福建工程学院数理系,福建福州,350108 |
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| 摘 要： | 通过研究二次型的性质,利用正(负)定矩阵判断多元函数的极值、证明不等式,由矩阵的特征值求多元函数的最值,再借助非退化线性替换进行多项式因式分解和判断二次曲线的形状,展现线性代数中的二次型知识在初等数学及微积分中的应用。
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| 关 键 词： | 二次型 正定矩阵 非退化线性替换 |
Applications of properties of quadratic form |
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| Xue Ronghua.Applications of properties of quadratic form[J].Journal of Fujian University of Technology,2011,9(3):273-275. |
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| Authors: | Xue Ronghua |
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| Institution: | Xue Ronghua(Mathematics and Physics Department,Fujian University of Technology,Fuzhou 350108,China) |
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| Abstract: | Based on the properties of quadratic form,extreme values of multi-variable functions were resolved by using positive/negative definite matrices.Inequality was proved.The optimal values of multi-variable function were solved through the eigenvalue of a matrix.The factorization of polynomial was conducted.The shape of quadratic curve was determined via non-degenerate linear transformation.The applications of the quadratic form of linear algebra are shown in calculus and elementary mathematics. |
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| Keywords: | quadratic form positive definite matrix non-degenerate linear transformation |
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