Number of characteristic polynomials of matrices with bounded height

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-02-19 DOI:10.1016/j.laa.2025.02.012

László Mérai , Igor E. Shparlinski

引用次数: 0

Abstract

We consider the set

M_{n} (Z; H)

n \times n

-matrices with integer elements of size at most H and obtain upper and lower bounds on the number of distinct irreducible characteristic polynomials which correspond to these matrices and thus on the number of distinct eigenvalues of these matrices. In particular, we improve some results of A. Abrams, Z. Landau, J. Pommersheim and N. Srivastava (2022).

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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.