Algebraic proof methods for identities of matrices and operators: Improvements of Hartwig’s triple reverse order law
作者：
Highlights：
• We illustrate a recent method for proving identities of matrices and linear operators.
• Computations are done in an abstract ring ignoring domains and codomains.
• The theory ensures that identities are also valid in terms of matrices or operators.
• We prove and generalize Hartwig’s result on three Moore-Penrose inverses.
• Both hand-made and computer-assisted proofs with the package OperatorGB are discussed.
摘要
•We illustrate a recent method for proving identities of matrices and linear operators.•Computations are done in an abstract ring ignoring domains and codomains.•The theory ensures that identities are also valid in terms of matrices or operators.•We prove and generalize Hartwig’s result on three Moore-Penrose inverses.•Both hand-made and computer-assisted proofs with the package OperatorGB are discussed.
论文关键词：Matrices and linear operators,Algebraic operator identities,Generalized inverses,Reverse order law,Automated proofs,Noncommutative polynomials,Quiver representations
论文评审过程：Received 22 July 2020, Revised 31 October 2020, Accepted 5 May 2021, Available online 3 July 2021, Version of Record 3 July 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126357
