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。
Based resolved by using on the properties of quadratic form, extreme values of multi-variable functions were positive/negative definite matrices. Inequali multi-variable function were solved through the eigenvalue ty was proved. The optimal values of 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.
出处
《福建工程学院学报》
CAS
2011年第3期273-275,共3页
Journal of Fujian University of Technology
关键词
二次型
正定矩阵
非退化线性替换
quadratic form
positive definite matrix
non-degenerate linear transformation
