Abstract
We consider proof certificates for identities of rectangular matrices. To automate their construction, we introduce an algebraic framework and supply explicit algorithms relying on non-commutative Grobner bases. We address not only verification, but also exploration and reasoning towards establishing new identities and even proving mathematical properties. Especially Grobner-driven elimination theory navigates us to insightful conclusions. We present several applications, that is efficiently formalized proofs for important identities of matrices: cancellation properties of triple products with Moore–Penrose pseudoinverses, a generalized Sherman–Morrison–Woodbury formula and an automated derivation of feedback loops in the famous Youla controller parametrization from control theory.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
