Representations and geometrical properties of generalized inverses over fields
In this paper, as a generalization of Urquhart’s formulas, we present a full description of the sets of inner inverses and (B, C)-inverses over an arbitrary field. In addition, identifying the matrix vector space with an affine space, we analyze geometrical properties of the main generalized inverse...
| Authors: | , , , , |
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| Format: | article |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/50372 |
| Online Access: | http://hdl.handle.net/10017/50372 https://dx.doi.org/10.1080/03081087.2021.1985420 |
| Access Level: | Open access |
| Keyword: | Outer inverses Inner inverses Moore-Penrose inverse (B, C) inverse Affine subspaces Urquhart's formula Matemáticas Mathematics |
| Summary: | In this paper, as a generalization of Urquhart’s formulas, we present a full description of the sets of inner inverses and (B, C)-inverses over an arbitrary field. In addition, identifying the matrix vector space with an affine space, we analyze geometrical properties of the main generalized inverse sets. We prove that the set of inner inverses, and the set of (B, C)-inverses, form affine subspaces and we study their dimensions. Furthermore, under some hypotheses, we prove that the set of outer inverses is not an affine subspace but it is an affine algebraic variety. We also provide lower and upper bounds for the dimension of the outer inverse set. |
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