矩阵与算子恒等式的代数证明方法：Hartwig三重反序律的改进
Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law
AI总结：
本文以Hartwig三重反序律为例，利用代数证明框架和软件包OperatorGB，在带对合的环中改进了广义逆的结果，并讨论了基于非交换多项式计算的计算机辅助证明。
摘要：
在改进广义逆的相关结果时，目标通常是在尽可能一般的设定下进行，即消除多余的假设并简化陈述中的某些条件。本文以著名的Hartwig三重反序律为例，展示如何使用近期的代数证明框架和软件包OperatorGB来实现这一点。我们对Hartwig结果的改进是在带对合的环中证明的，并讨论了基于该框架以及单次非交换多项式计算来证明这些结果在其他设定中成立的计算机辅助证明。
英文摘要：
When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some of the conditions in statements. In this paper, we use Hartwig's well-known triple reverse order law as an example for showing how this can be done using a recent framework for algebraic proofs and the software package OperatorGB. Our improvements of Hartwig's result are proven in rings with involution and we discuss computer-assisted proofs that show these results in other settings based on the framework and a single computation with noncommutative polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
