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高等数学与初等数学有着密切的联系,其中有些基本原理对中学数学问题的解决有着很强的指导意义,能对问题给出一般性的解决方法,便于掌握。本文旨在探讨二次型理论一定理在中学数学中的应用。一、定理在北京大学数学力学系编《高等代数》教科书第375页有这么一个结论:设f(x1,x2,……xn)=X’AX是一实二次型,λ1,λ2……,λn是A的特征多项式的根,且λ1≤λ2≤…≤λn。且λ1X’X≤
Higher mathematics and elementary mathematics are closely linked, some of which are basic principles of mathematical problems in high school have a strong guiding significance, can give a general solution to the problem, easy to grasp. The purpose of this paper is to explore the application of the theorem of quadratic theory in high school mathematics. First, the theorem in the Department of Mathematical Mechanics, Peking University, “Advanced Algebra” textbook, page 375 has such a conclusion: Let f (x1, x2, ... ... xn) = X’AX is a real quadratic, λ1, λ2 , λn is the root of the characteristic polynomial of A, and λ1≤λ2≤ ... ≤λn. And λ1X’X≤