关于二次型的介值性

On the Intermediate Characteristic of Quadratic Forms

根据代数学中二次型的许多重要性质以及连续函数和导函数的介值性,提出二次型的介值性定理,通过使用非退化线性替换把二次型化为规范形的方法,证明介值性定理的正确性.

This paper presents an existence theorem of intermediate value over quadratic forms according to many important characteristics of quadratic forms introduced in algebra and the intermediate characteristic of continuous functions and derivative functions. The result is proved by transforming quadratic forms to their normal forms via some nondeyenerate linear substitutions.