Chocano Feito, Pedro J.2025-09-222025-09-222025-09-09Pedro J. Chocano, Eigenvalues and signature of quadratic forms associated with finite topological spaces, Linear Algebra and its Applications, Volume 728, 2026, Pages 263-282, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2025.09.007.0024-3795https://hdl.handle.net/10115/102357Given any finite topological space X and a field K, we associate a quadratic space (QX,VX), consisting of a vector space VXover Kand a quadratic form QX:VX×VX→K, to X. The eigenvalues and signature of QXare topological invariants of X. We study their relations with X. From this, we obtain restrictions to check whether a finite topological space can be embedded into another one. Additionally, we compute these invariants for minimal finite models of spheres and other families of finite spaces.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/PosetsFinite topological spaceQuadratic formEigenvaluesSignatureArticlehttps://doi.org/10.1016/j.laa.2025.09.007info:eu-repo/semantics/openAccess