特殊矩阵特征值的Wielandt-Hoffman-残差型扰动界  

Wielandt-Hoffman-residual Type Perturbation Boundsfor Eigenvalues of Special Matrices

作　　者：孔祥强 KONG Xiangqiang(School of Mathematics and Statistics, Heze University, Heze 274015,China)

机构地区：[1]菏泽学院数学与统计学院,山东菏泽274015

出　　处：《贵州大学学报（自然科学版）》2020年第3期6-9,共4页Journal of Guizhou University:Natural Sciences

基　　金：山东省自然科学基金项目资助(ZR201709250116,ZR2017MA029);菏泽学院科研基金科技计划项目资助(XY17KJ02);菏泽学院大学数学课程混合式教学模式研究与实践项目资助(2018311)。

摘　　要：利用矩阵的分块及矩阵的奇异值分解,探讨了矩阵及其扰动后的矩阵阶数不同时特征值的扰动界,得到了Hermite矩阵特征值的Wielandt-Hoffman-残差型扰动界。进一步将所得结果推广到可对称化矩阵,给出了可对称化矩阵特征值新的Wielandt-Hoffman-残差型扰动界,且所得结论推广了原有结果。By using the partitioning of matrices and the singular value decomposition of matrices,the perturbation eigenvalues bounds of matrix and its disturbed matrix with different order were discussed.The Wielandt-Hoffman-residual type perturbation bounds for the eigenvalues of Hermite matrices were obtained.And the conclusion is further extended to the symmetrizable matrix.A new Wielandt-Hoffman-residual type perturbation bound for the symmetrizable matrix was given,and the conclusion obtained extends the original results.

关 键 词：HERMITE矩阵 可对称化矩阵 奇异值分解 特征值 

分 类 号：O241.6[理学—计算数学]