论文标题
代数证明矩阵和操作员身份的证明方法：Hartwig的三重反向订单定律的改进
Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law
论文作者
论文摘要
当改善广义反相的结果时，目的通常是通过消除多余的假设并简化语句中的某些条件来实现这一目标。在本文中，我们使用Hartwig众所周知的三重反订单定律作为一个示例，用于展示如何使用代数证明的最新框架和软件包操作员进行操作。我们对Harartwig的结果的改进在环中得到了证明，我们讨论了计算机辅助的证据，这些证据基于框架和单一的计算在其他设置中显示了这些结果，并具有非交换性多项式的单一计算。
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.
