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Research Article

Lattice properties of partial orders for complex matrices via orthogonal projectors

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Pages 718-736 | Received 08 Jun 2022, Accepted 06 Oct 2022, Published online: 26 Dec 2022

References

  • Baksalary OM, Trenkler G. Core inverse of matrices. Linear Multilinear Algebra. 2010;58(5–6):681–697. DOI:10.1080/03081080902778222
  • Ben-Israel A, Greville TNE. Generalized inverses: theory and applications. 2nd ed. New York: Springer-Verlag; 2003. (CMS books in mathematics/ouvrages de mathématiques de la SMC; vol. 15).
  • Campbell SL, Meyer Jr CD, Generalized inverses of linear transformations. New York: Dover Publications Inc.; 1991. Corrected reprint of the 1979 original.
  • Chen J, Zhu H, Patricio P, et al. Characterizations and representations of core and dual core inverses. Canad Math Bull. 2017;60(2):269–282. DOI:10.4153/CMB-2016-045-7
  • Kyrchei I. Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field. Appl Math Comput. 2015;264:453–465. DOI:10.1016/j.amc.2015.04.125
  • Pablos Romo F. On Drazin–Moore–Penrose inverses of finite potent endomorphisms. Linear Multilinear Algebra. 2021;69(4):627–647. DOI:10.1080/03081087.2019.1612834
  • Wang H, Liu X. Characterizations of the core inverse and the core partial ordering. Linear Multilinear Algebra. 2015;63(9):1829–1836. DOI:10.1080/03081087.2014.975702
  • Zhou M, Chen J, Stanimirovic PS, et al. Complex varying-parameter Zhang neural networks for computing core and core-EP inverse. Neural Process Lett. 2020;51(2):1299–1329. DOI:10.1007/s11063-019-10141-6
  • Zhu H, Patrício P. Several types of one-sided partial orders in rings. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM. 2019;113(4):3177–3184. DOI:10.1007/s13398-019-00685-6
  • Drazin MP. Natural structures on semigroups with involution. Bull Amer Math Soc. 1978;84(1):139–141. DOI:10.1090/S0002-9904-1978-14442-5
  • Baksalary JK, Mitra SK. Left-star and right-star partial orderings. Linear Algebra Appl. 1991;149:73–89. DOI:10.1016/0024-3795(91)90326-R
  • Cvetković-Ilić DS, Mosić D, Wei Y. Partial orders on B(H). Linear Algebra Appl. 2015;481:115–130. DOI:10.1016/j.laa.2015.04.025
  • Manjunatha Prasad K, Mohana KS, Sheela YS. Matrix partial orders associated with space preorder. In: Combinatorial matrix theory and generalized inverses of matrices. New Delhi: Springer; 2013. p. 195–226.
  • Mitra SK, Bhimasankaram P, Malik SB. Matrix partial orders, shorted operators and applications. Hackensack (NJ): World Scientific Publishing Co. Pte. Ltd.; 2010. (Series in algebra; vol. 10).
  • Burris S, Sankappanavar HP. A course in universal algebra. New York-Berlin: Springer-Verlag; 1981. (Graduate texts in mathematics; vol. 78).
  • Cīrulis J. One-sided star partial orders for bounded linear operators. Oper Matrices. 2015;9(4):891–905. DOI:10.7153/oam-09-52
  • Antezana J, Cano C, Mosconi I, et al. A note on the star order in Hilbert spaces. Linear Multilinear Algebra. 2010;58(7–8):1037–1051. DOI:10.1080/03081080903227104
  • Djikić MS. Lattice properties of the core-partial order. Banach J Math Anal. 2017;11(2):398–415. DOI:10.1215/17358787-0000010X
  • Malik SB, Rueda L, Thome N. Further properties on the core partial order and other matrix partial orders. Linear Multilinear Algebra. 2014;62(12):1629–1648. DOI:10.1080/03081087.2013.839676
  • Hartwig RE, Spindelböck K. Matrices for which A∗ and A† commute. Linear Multilinear Algebra. 1983;14(3):241–256. DOI:10.1080/03081088308817561
  • Hartwig RE, Drazin MP. Lattice properties of the *-order for complex matrices. J Math Anal Appl. 1982;86(2):359–378. DOI:10.1016/0022-247X(82)90228-1
  • Eagambaram N, Manjunatha Prasad K, Mohana KS. Column space decomposition and partial order on matrices. Electron J Linear Algebra. 2013;26:795–815. DOI:10.13001/1081-3810.1688
  • Xu XM, Du HK, Fang X, et al. The supremum of linear operators for the *-order. Linear Algebra Appl. 2010;433(11–12):2198–2207. DOI:10.1016/j.laa.2010.07.026
  • Hartwig RE. Pseudolattice properties of the star-orthogonal partial ordering for star-regular rings. Proc Amer Math Soc. 1979;77(3):299–303. DOI:10.2307/2042174
  • Djikić MS. Properties of the star supremum for arbitrary Hilbert space operators. J Math Anal Appl. 2016;441(1):446–461. DOI:10.1016/j.jmaa.2016.04.020