目 录摘 要………………………………………………………………… 1引言…………………………………………………………………… 21.二次型的相关定义与定理………………………………………… 32.二次型的应用……………………………………………………… 6 2.1 在二次曲线中的应用…………………………………………………… 6 2.2 在证明不等式中的应用………………………………………………… 7 2.3 在求极值中的应用……………………………………………………… 8 2.4 在求某些曲线或曲面积分中的应用…………………………………… 10 2.5 在多项式因式分解中的应用……………………………………………10参考文献……………………………………………………………… 12致…………………………………………………………………… 13浅谈二次型与其应用摘 要：二次型是高等代数的重要容之一，通过讨论二次型的结构与性质，解决一些不等式的证明、求极值、因式解等初等问题.并比较正交变换和配方法化二次型为标准型的区别，给出了二次型在计算某些积分中的应用.再借助非退化线性替换推断二次曲线的形状，展现线性代数中的二次型知识在微积分中的应用.关键词：二次型；正定矩阵；非退化线性替换；标准型；正交变换A Talk about Quadric Form and Its ApplicationAbstract: the quadric form is one of the important contents of higher algebra, through the study of the structure and the quadratic nature, solve some inequality proof, for extreme, factoring in elementary problems and solutions. And compared with orthogonal transformation method HuaEr times and the difference between the standard model, and gives the second type in the calculation of the application of some points. Again the degradation of linear replace judgment by the shape of the quadratic curves, show linear algebra in the second type of the application of the knowledge in the calculus. Key Words: Quadratic; Positive definite matrix; The degradation of linear replacement; Standard; Orthogonal transformation 引言高等代数与初等代数的联系是密不可分的，在中学数学中，不等式...
