Eigenvalues and signature of quadratic forms associated with finite topological spaces

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-09 DOI:10.1016/j.laa.2025.09.007

Pedro J. Chocano

引用次数: 0

Abstract

Given any finite topological space X and a field

K

, we associate a quadratic space

(Q_{X}, V_{X})

, consisting of a vector space

V_{X}

over

K

and a quadratic form

Q_{X} : V_{X} \times V_{X} \to K

, to X. The eigenvalues and signature of

Q_{X}

are 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.

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有限拓扑空间二次型的特征值与特征

给定一个有限拓扑空间X和一个域K，我们将一个由K上的向量空间VX和二次形式QX:VX×VX→K组成的二次空间（QX，VX）关联到X。QX的特征值和签名是X的拓扑不变量，我们研究了它们与X的关系。由此得到了检验一个有限拓扑空间能否嵌入到另一个有限拓扑空间中的限制条件。此外，我们计算了球面和其他有限空间族的最小有限模型的不变量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.