Complex Structures on Real Vector Spaces
DOI:
https://doi.org/10.14393/BEJOM-v5-2024-73258Keywords:
Complex structure, complex vector spaces, linear algebraAbstract
In this article, complex structures in real vector spaces are studied from an algebraic perspective. One of the main results guarantees the existence and uniqueness of complex structures, up to equivalence, in spaces of even dimension or infinite dimension. Additionally, a description of the set of complex structures as a homogeneous space of the general linear group is presented, and finally, it is shown how to construct complex structures in some different settings from known complex structures. There is a lack of a comprehensive and detailed text in the literature with complete proofs of these results, and one of the objectives of this article is precisely to help fill this gap.
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Copyright (c) 2024 Daniel Rotmeister, Laércio dos Santos
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