Statistics of ranks, determinants and characteristic polynomials of rational matrices

Autor:	Afifurrahman, Muhammad, Kuperberg, Vivian, Ostafe, Alina, Shparlinski, Igor E.
Rok vydání:	2024
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	We consider the set of $n\times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matrices of a given rank and then apply them to count such matrices with a given determinant, or a given characteristic polynomial.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.10086 Zobrazit plný text záznamu View this record from Arxiv