Statistics of ranks, determinants and characteristic polynomials of rational matrices
Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. 2024. Statistics of ranks, determinants and characteristic polynomials of rational matrices. Forum Mathematicum. 37(4).
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Author
Afifurrahman, Muhammad;
Kuperberg, Vivian ZieveISTA;
Ostafe, Alina;
Shparlinski, Igor E.
Abstract
We consider the set of 𝑚×𝑛 matrices with rational entries having numerator and denominator of size at most H and obtain various upper bounds on the number of such matrices of a given rank, or with a given determinant, or a given characteristic polynomial. We also consider similar questions for matrices whose entries are Egyptian fractions.
Publishing Year
Date Published
2024-01-01
Journal Title
Forum Mathematicum
Publisher
De Gruyter
Volume
37
Issue
4
ISSN
eISSN
IST-REx-ID
Cite this
Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. Statistics of ranks, determinants and characteristic polynomials of rational matrices. Forum Mathematicum. 2024;37(4). doi:10.1515/forum-2024-0114
Afifurrahman, M., Kuperberg, V. Z., Ostafe, A., & Shparlinski, I. E. (2024). Statistics of ranks, determinants and characteristic polynomials of rational matrices. Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2024-0114
Afifurrahman, Muhammad, Vivian Zieve Kuperberg, Alina Ostafe, and Igor E. Shparlinski. “Statistics of Ranks, Determinants and Characteristic Polynomials of Rational Matrices.” Forum Mathematicum. De Gruyter, 2024. https://doi.org/10.1515/forum-2024-0114.
M. Afifurrahman, V. Z. Kuperberg, A. Ostafe, and I. E. Shparlinski, “Statistics of ranks, determinants and characteristic polynomials of rational matrices,” Forum Mathematicum, vol. 37, no. 4. De Gruyter, 2024.
Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. 2024. Statistics of ranks, determinants and characteristic polynomials of rational matrices. Forum Mathematicum. 37(4).
Afifurrahman, Muhammad, et al. “Statistics of Ranks, Determinants and Characteristic Polynomials of Rational Matrices.” Forum Mathematicum, vol. 37, no. 4, De Gruyter, 2024, doi:10.1515/forum-2024-0114.
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