JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (3): 19-24.doi: 10.6040/j.issn.1671-9352.0.2022.167

Previous Articles     Next Articles

Weak core inverse of core-EP decomposition

CHENG Yang, CUI Yu-ru   

  1. College of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China
  • Published:2023-03-02

Abstract: Based on core-EP decomposition of a matrix, the weak core inverse of a complex matrix is studied. For a complex matrix A, a new representation of the weak core inverse A,+ of A is given, and some equivalent characterizations of AA,+=A,+A are presented, as well as the relation between(Am),+ and(A,+)m is investigated.

Key words: weak core inverse, core-EP decomposition, weak group inverse, DMP inverse

CLC Number: 

  • O151.21
[1] PENROSE R. A generalized inverse for matrices[J]. Proc Cambridge Philos Soc, 1955, 51:406-413.
[2] BEN-ISRAEL A, GREVILLE T N E. Generalized inverses: theory and applications[M]. New York: Spring-Verlag, 2003: 163-172.
[3] MANJUNATHA P K, MOHANA K S. Core-EP inverse[J]. Linear & Multilinear Algebra, 2014, 62(6):792-802.
[4] WANG Hongxing, CHEN Jianlong. Weak group inverse[J]. Open Mathematics, 2018, 16(1):1218-1232.
[5] MALIK S B, THOME N. On a new generalized inverse for matrices of an arbitrary index[J]. Applied Mathematics and Computation, 2014, 226:575-580.
[6] FERREYRA D E, LEVIS F E, PRIORI A N, et al. The weak core inverse[J]. Aequationes Mathematicae, 2021, 95(2):351-373.
[7] FU Zhimei, ZUO Kezheng, CHEN Yang. Further characterizations of the weak core inverse of matrices and the weak core matrix[J]. AIMS Math, 2022, 7(3):3630-3647.
[8] WANG Hongxing. Core-EP decomposition and Its applications[J]. Linear Algebra and Its Application, 2016, 508(1):289-300.
[9] HARTWIG R E, SPINDELBÖCK K. Matrices for which A* and A+ commute[J]. Linear & Multilinear Algebra, 1983, 14(3):241-256.
[10] FERREYRA D E, LEVIS F E, THOME N. Maximal classes of matrices determining generalized inverses[J]. Applied Mathematics and Computation, 2018, 333:42-52.
[1] JIAN Yuan, LIU Ding-you. Extremal eigenvalues of a class of tridiagonal interval matrices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 15-22.
[2] LING Si-Chao, CHENG Wue-Han, WEI Mu-Sheng. On Hermitian solutions to general linear quaternionic matrix equations [J]. J4, 2008, 43(12): 1-4.
[3] SONG Cai-qin,ZHAO Jian-li,LI Dong-fang . The reverse order law for (T,S,2)-inverse of a matrix semi-tensor product [J]. J4, 2008, 43(6): 71-76 .
[4] ZHAO Jian-li,LI Ying and ZHANG Li-mei . QR decomposition and the equality constrained least squares problem over a quaternion field [J]. J4, 2007, 42(6): 65-68 .
[5] HU Fu-gao,ZENG Yu-e .

Identities and application of the rank of a class of matrices polynomials

[J]. J4, 2008, 43(8): 51-54 .
[6] YUAN Hun-ping . Schur factorization and normal matrices factorization of row (column) symmetric matrices [J]. J4, 2007, 42(10): 123-126 .
[7] WANG Ting-ming,LI Bo-tang . Proof of a class of matrix rank identities [J]. J4, 2007, 42(2): 43-45 .
[8] JIA Zhi-gang,ZHAO Jian-li,ZHANG Feng-xia . Eigen-problem and singular value decomposition of the generalized symmetric matrix [J]. J4, 2007, 42(12): 15-18 .
[9] CHENG Yan-liang, SHAO Yong. Semiring varieties defined by Greens relations on a semiring [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 1-7.
[10] YIN Jiao-jiao, SHAO Yong, HAN Jin. e-invertible matrices over antirings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 67-73.
[11] ZHAO Ya-qi, REN Fang-guo. Representation of matrices and its applications to entropy [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(11): 97-104.
[12] WANG Jun-ling, SHAO Yong. Greens relations on a class of semiring which multiplicative reduct is an idempotent semigroup [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(6): 15-22.
[13] DENG Wei-na, ZHAO Xian-zhong. Linear operators preserving transitive closures of matrices over the binary Boolean semiring [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 64-70.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!