有理矩阵有理正交对角化的计算机实现

Using the Computer to Realize the Rational Orthogonal Diagonalization of the Rational Matrix

有理对称矩阵在有理数域上的正交对角化过程不仅步骤繁琐,而且当矩阵阶数较大时计算量急剧增大,致使人工操作很难实现,所以需要计算机辅助操作。然而已有的数学软件在此问题的计算上存在着误差,因此采用分数运算手段,设计了求矩阵特征根、特征向量、正交化和单位化的算法及C语言程序,使用该程序能够精确地判定及求解有理矩阵在有理数域上的正交对角化问题。

The step of orthogonal diagonalization process of the rational symmetric matrix in the rational number field is not only cumbersome, and when the matrix order is large, the amount of calculation is very large, the manual operation is difficult to implement, so we need the auxiliary operation of computer. But there is a error in the calculation with the existing mathematical software, so we use the method of fractional arithmetic to design the algorithm for the matrix characteristic root, feature vector, orthogonalization and unitization and C language program. Using this program can accurately judge and solve the orthogonal diagonalization of the rational matrix in the rational number field.