一种计算实对称矩阵特征向量的矩阵扩张算法

Matrix extension for computing eigenvectors of real symmetric matrix

提出了一种用矩阵扩张求实对称矩阵的特征向量的方法,将传统的通过求解齐次线性方程组得到特征向量转化为矩阵扩张问题来求解特征向量.算法表明,这一算法具有快速、易于计算机实现及无需Gram-Schmidt正交化即可得到互相正交的单位特征向量等优点.

The paper presents a practical method of computing the eigenvectors of real symmetric matrix by matrix extension.This method transfers the solving of characteristic equation to extending it to an n×n orthogonal matrix to obtain the eigenvectors.It can be seen that this method is easily implemented in the computer and does not need the standard Gram-Schmidt orthogonalization process.