用实对称矩阵的正定性研究空间二次曲面

The Research of Dimensional Conicoide by Using the Orthogonality of Real Symmetric Matrix

空间二次曲面是一类特殊的、结构简单的空间曲面。每一个二次曲面与一个三元二次方程F(x,y,z)=0一一对应,(x,y,z)是二次曲面上任意一点的坐标。然而方程F(x,y,z)=0系数作正交性的变化,例如旋转、平移、对称等并不会改变空间曲面的形状。因此,通过讨论方程F(x,y,z)=0系数的正交性的变化变化,就可以很好地研究空间二次曲面的形状。

Dimensional conicoide is a special curved surface with simple structures . Every geometric surface and a ternary quadratic equation F（ x, y, z） = 0 is one to one corresponding and （ x, y, z） is a coordinate of any point on geometric surface. However, when the quofiety of the equation F（ x, y, z） = 0 makes orthogonality change, such as rotation,translation and symmetry, the form of dimensional surface can/t be changed. Therefore, the form of dimensional conicoide can be well researched by discussing the orthogonally change of the quotiety of the equation F（ x, y, z） = 0.