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Generalized inverses of matrices over skew polynomial rings

The applications of generalized inverses of matrices appear in many fields like applied mathematics, statistics and engineering [2]. In this thesis, we discuss generalized inverses of matrices over Ore polynomial rings (also called Ore matrices).

We first introduce some necessary and sufficient conditions for the existence of {1}-, {1,2}-, {1,3}-, {1,4}- and MP-inverses of Ore matrices, and give some explicit formulas for these inverses. Using {1}-inverses of Ore matrices, we present the solutions of linear systems over Ore polynomial rings. Next, we extend Roth's Theorem 1 and generalized Roth's Theorem 1 to the Ore matrices case. Furthermore, we consider the extensions of all the involutions ψ on R(x), and construct some necessary and sufficient conditions for ψ to be an involution on R(x)[D;σ,δ]. Finally, we obtain two different explicit formulas for {1,3}- and {1,4}-inverses of Ore matrices.

The Maple implementations of our main algorithms are presented in the Appendix. / May 2017

Identiferoai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/32173
Date30 March 2017
CreatorsFeng, Qiwei
ContributorsZhang, Yang (Mathematics), Kucera, Tommy (Mathematics) Mandal, Saumen (Statistics)
Source SetsUniversity of Manitoba Canada
Detected LanguageEnglish

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