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[1]杨虹,钟金,马柏林.矩阵核心逆的Sherman-Morrison-Woodbury公式及其应用[J].江西理工大学学报,2021,42(01):98-104.[doi:10.13265/j.cnki.jxlgdxxb.2021.01.014]
 YANG Hong,ZHONG Jin,MA Bolin.Sherman-Morrison-Woodbury formula for the core inverse of matrices and its applications[J].Journal of Jiangxi University of Science and Technology,2021,42(01):98-104.[doi:10.13265/j.cnki.jxlgdxxb.2021.01.014]


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矩阵核心逆的Sherman-Morrison-Woodbury公式及其应用(/HTML)
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《江西理工大学学报》[ISSN:2095-3046/CN:36-1289/TF]

卷:
42卷
期数:
2021年01期
页码:
98-104
栏目:
出版日期:
2021-02-28

文章信息/Info

Title:
Sherman-Morrison-Woodbury formula for the core inverse of matrices and its applications
文章编号:
2095-3046(2021)01-0098-05
作者:
杨虹12 钟金1 马柏林2
(1. 江西理工大学理学院,江西 赣州 341000; 2. 嘉兴学院数理与信息工程学院, 浙江 嘉兴 314001)
Author(s):
YANG Hong12 ZHONG Jin1 MA Bolin2
(1. Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi, China; 2. School of Mathematics and Information Engineering, Jiaxing University, Jiaxing 314001, Zhejiang, China)
关键词:
核心逆值域Sherman-Morrison-Woodbury公式非负性
分类号:
O151.21
DOI:
10.13265/j.cnki.jxlgdxxb.2021.01.014
文献标志码:
A
摘要:
为了建立矩阵核心逆的Sherman-Morrison-Woodbury公式,文章利用值域与核的包含关系给出了矩阵A-YGZT的核心逆的表达式,推广了经典的Sherman-Morrison-Woodbury公式,并利用所得结果讨论了扰动矩阵A-YGZT的核心逆的非负性。

参考文献/References:

[1] SHERMAN J, MORRISON W J. Adjustment of an inverse matrix corresponding to a change in one element of a given matrix[J]. The Annals of Mathematical Statistics, 1950, 21(1):124-127.[2] WOODBURY M. Inverting modified matrices[M]. Technical Report 42, Statistical Research Group, Princeton University, Princeton, NJ, 1950.[3] BARTLETT M S. An inverse matrix adjustment arising in discriminant analysis[J]. The Annals of Mathematical Statistics, 1951, 22(1):107-111.[4] BODEWIG E. Matrix calculus[M]. North-Holland, Amsterdam, 1959.[5] HAGER W W. Updating the inverse of a matrix[J]. SIAM Review, 1989, 31(2): 221-239. [6] EGIDI N, MAPONI P. A Sherman-Morrison approach to the solution of linear systems[J]. Journal of Computational and Applied Mathematics, 2006, 189(1/2):703-718.[7] 过美林, 钟金. 两类2-Toeplitz型矩阵的奇异值[J]. 江西理工大学学报, 2020, 41(1):97-100.[8] DENG C Y. A generalization of the Sherman-Morrison-Woodbury formula[J]. Applied Mathematics Letters, 2011, 24(9):1561-1564.[9] DENG C Y, WEI Y M. Some new results of Sherman-Morrison-Woodbury formula[C]. Proceeding of the Sixth International Conference of Matrices and Operators, 2014, 2:230-233.[10] KOLUND?IJA M Z. Generalized Sherman-Morrison-Woodbury formula for the generalized Drazin inverse in Banach algebra[J]. Filomat, 2017, 31(16):5159-5167.[11] 魏什笛, 杜法鹏. A-XGY的Moore-Penrose逆的表示[J]. 高等学校计算数学学报, 2015, 37(3):228-233.[12] WANG G R, WEI Y M, QIAO S Z. Generalized inverses: Theory and Computations[M]. Springer, Singapore, 2018. [13] BAKSALARY O M, TRENKLER G. Core inverse of matrices[J]. Linear and Multilinear Algebra, 2010, 58(6): 681-697.[14] WANG H X, LIU X J. Characterizations of the core inverse and the core partial ordering[J]. Linear and Multilinear Algebra, 2015, 63(9):1829-1836.[15] ZOU H L, CHEN J L, PATRíCIO P. Reverse order law for the core inverse in rings[J]. Mediterranean Journal of Mathematics, 2018, 15(3):1-17.[16] KE Y Y, WANG L, CHEN J L. The core inverse of a product and matrices[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42(1):51-66.[17] ZHOU M M, CHEN J L, ZHU X. The group inverse and core inverse of sums of two elements in a ring[J]. Communications in Algebra, 2020, 48(2):676-690.[18] MALIK S B, RUEDA L, THOME N. Further properties on the core partial order and other matrix partial orders[J]. Linear and Multilinear Algebra, 2014, 62(12):1629-1648. [19] BERMAN A, PLEMMONS R J. Cones and iterative methods for best least squares solutions of linear systems[J]. SIAM Journal on Numerical Analysis, 1974, 11(1):145-154.

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备注/Memo

备注/Memo:
收稿日期:2020-10-08
基金项目:国家自然科学基金资助项目(11661041);江西理工大学清江青年优秀人才项目(JXUSTQJYX2017007)
作者简介:杨虹(1995— ),女,硕士研究生,主要从事矩阵论等方面的研究。E-mail: 2521791193@qq.com

更新日期/Last Update: 1900-01-01