关于同时化一对实二次型为标准形的探讨

To Transform A Pair of Real Quadratic Forms Into Standard Forms

给出一对同阶实对称矩阵A、B,存在正交矩阵P使A,B同时对角化的充分必要条件;进一步给出存在正交替换同时化一对实二次型为标准形的充分必要条件。

This paper gives the necessary and sufficient condition for existing an orthogonal matrix P to transform a pair of real symmetric matrices A, B (with same order) into diagonal, and gives the necessary and sufficient condition for existing an orthogonal transformation to transform a pair of real quadratic forms into standard forms.