Representations and symbolic computation of generalized inverses over fields

Predrag S. Stanimirović, Miroslav Ćirić, Alberto Lastra, Juan Rafael Sendra and Juana Sendra

Applied Mathematics and Computation, 2021, vol. 406, issue C

Abstract: This paper investigates representations of outer matrix inverses with prescribed range and/or null space in terms of inner inverses. Further, required inner inverses are computed as solutions of appropriate linear matrix equations (LME). In this way, algorithms for computing outer inverses are derived using solutions of appropriately defined LME. Using symbolic solutions to these matrix equations it is possible to derive corresponding algorithms in appropriate computer algebra systems. In addition, we give sufficient conditions to ensure the proper specialization of the presented representations. As a consequence, we derive algorithms to deal with outer inverses with prescribed range and/or null space and with meromorphic functional entries.

Keywords: Outer inverse; Inner inverse; Matrix equation; Computer algebra; Specialization of matrices; Matrices with functional entries (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003763

DOI: 10.1016/j.amc.2021.126287

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