Positive moments forever: Undecidable and decidable cases

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-21 DOI:10.1016/j.laa.2025.05.015

Gemma De les Coves , Joshua Graf , Andreas Klingler , Tim Netzer

引用次数: 0

Abstract

We investigate the generalized moment membership problem for matrices, a formulation equivalent to Skolem's problem for linear recurrence sequences. We show decidability for orthogonal, unitary, and real eigenvalue matrices, and undecidability for matrices over certain commutative and non-commutative polynomial rings. As consequences, we deduce that positivity is decidable for simple unitary linear recurrence sequences and undecidable for linear recurrence sequences over commutative polynomial rings. As a byproduct, we also prove a free version of Pólya's theorem.

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永远的积极时刻：不确定和可决定的案件

我们研究了矩阵的广义矩隶属度问题，一个等价于线性递归序列的Skolem问题的公式。我们证明了正交、酉和实特征值矩阵的可判性，以及矩阵在某些可交换和非可交换多项式环上的不可判性。作为结果，我们推导出简单酉线性递归序列的正性是可判定的，而对交换多项式环上的线性递归序列的正性是不可判定的。作为副产品，我们也证明了Pólya定理的一个免费版本。

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.