实对称矩阵正交特征向量的一种新解法  

A New Solution Method for Orthogonal Eigenvectors of Real Symmetric Matrices

作　　者：阚永志[1] KAN Yong-zhi(College of Science,Liaoning University of Technology,Jinzhou 121001,China)

机构地区：[1]辽宁工业大学理学院,辽宁锦州121001

出　　处：《辽宁工业大学学报（自然科学版）》2024年第3期206-210,共5页Journal of Liaoning University of Technology(Natural Science Edition)

摘　　要：为克服“只在给定向量组的条件下,才能求得正交向量组”的局限性,利用特征向量和正交的定义及齐次线性方程组的非零解求解方法,给出实对称矩阵对应于重特征值的正交特征向量的一种新的求解方法。研究表明,该方法可以有效地减少计算量,并可以直接写出实对称矩阵对应于重特征值的正交特征向量。In order to overcome the limitation that“orthogonal vector set can be obtained only under the conditions of given vector set”,a new solution method for orthogonal eigenvectors corresponding to multiple eigenvalues of real symmetric matrices is given by using the definition of eigenvectors and orthogonality and the non-zero solution of homogeneous linear equations.The result shows that the proposed method can reduce the amount of computation effectively,and can directly write the orthogonal eigenvectors corresponding to the multiple eigenvalues of the real symmetric matrices.

关 键 词：实对称矩阵 Schmidt正交化过程 正交 特征向量 齐次线性方程组 非零解 

分 类 号：O151.2[理学—数学]