四面体幂级数的上限

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-11-19 DOI:10.1016/j.laa.2024.11.009

Cosimo Flavi

引用次数: 0

摘要

我们为任意二次函数形式的每个幂的秩建立了一个上限。具体来说，对于任意 s∈N，我们证明秩为 n 的二次函数形式的 s 次幂随 ns 增长。此外，我们还证明了对于所有 n>(2s-1)2，它的秩都是子代的。

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Upper bounds for the rank of powers of quadrics

We establish an upper bound for the rank of every power of an arbitrary quadratic form. Specifically, for any

s \in N

, we prove that the s-th power of a quadratic form of rank n grows as

n^{s}

. Furthermore, we demonstrate that its rank is subgeneric for all

n > {(2 s - 1)}^{2}

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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.