线性代数中的二次型应用

The Application of Quadratic Form in Linear Algebra

通过平面向量集合和空间向量集合的关系,方程组解的情况与平面的位置之间对应关系;用正交变换将含有n个变量的二次型化为只含有平方项的标准形;以及坐标轴的旋转关系与行列式在几何中的应用这几个方面,以实例说明线性代数在几何直观课程教学中的应用.

By the relation between the set of plane vectors and the set of space vectors, the corresponding relation between the solution of the system of equations and the position of the plane is obtained. Quadratic form with n variables is transformed into standard form with only square terms by orthogonal transformation. The application of the rotation relation of coordinate axis and determinant in geometry is also discussed. The application of linear algebra in geometry intuitive teaching is illustrated with examples.