Abstract
This paper deals with new generalized inverses of rectangular complex matrices, namely 1MP and MP1-inverses. They are constructed from oblique projectors represented by means of inner generalized inverses, by using an adequate equivalence relation, and then passing to the quotient set. We give characterizations and general expressions for 1MP and MP1-inverses. As applications, the binary relations induced for these new generalized inverses are proved to be partial orders.
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N. Thome is the Correspoding Author of this paper but not the Handling Editor.
M. V. Hernández and M. B. Lattanzi: Partially supported by Universidad Nacional de La Pampa, Facultad de Ingeniería (Grant Resol. Nro. 135/19).
N. Thome: Partially supported by Universidad Nacional de La Pampa, Facultad de Ingeniería (Grant Resol. Nro. 135/19), by Ministerio de Economía y Competitividad of Spain (grant Red de Excelencia MTM2017-90682-REDT), by Universidad Nacional del Sur of Argentina (Grant PGI 24/L108), and by Universidad Nacional de Río Cuarto (Grant Res. Nro. 083/2020).
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Hernández, M.V., Lattanzi, M.B. & Thome, N. From projectors to 1MP and MP1 generalized inverses and their induced partial orders. RACSAM 115, 148 (2021). https://doi.org/10.1007/s13398-021-01090-8
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DOI: https://doi.org/10.1007/s13398-021-01090-8