Арифметичні властивості коренів лінійних рівнянь
Анотація
Зразок для цитування: В. П. Щедрик, “Арифметичні властивості коренів лінійних рівнянь,” Мат. методи та фіз.-мех. поля, 65, No. 3-4, 44–49 (2022), https://doi.org/10.15407/mmpmf2022.65.3-4.44-49
Ключові слова
Посилання
V. P. Shchedryk, “Bezout ring of stable range 1.5,” Ukr. Mat. Zh., 67, No. 6, 849–860 (2015) (in Ukrainian); English translation: Ukr. Math. J., 67, No. 6, 960–974 (2015), https://doi.org/10.1007/s11253-015-1126-9
V. P. Shchedryk, “The left greatest common divisor and the left least common multiple for all solutions of the matrix equation BX=A over a commutative domain of elementary divisors,” Ukr. Mat. Zh., 73, No. 2, 261–267 (2021) (in Ukrainian), https://doi.org/10.37863/umzh.v73i2.6321; English translation: Ukr. Math. J., 73, No. 2, 303–310 (2021), https://doi.org/10.1007/s11253-021-01923-0
V. A. Bovdi, V. P. Shchedryk, “Generating solutions of a linear equation and structure of elements of the Zelisko group,” Linear Algebra Appl., 625, 55–67 (2021), https://doi.org/10.1016/j.laa.2021.04.019
V. A. Bovdi, V. P. Shchedryk, “Generating solutions of a linear equation and structure of elements of the Zelisko group II,” Quaestiones Mathematicae, 46, No. 9, 1789–1798 (2023), https://doi.org/10.2989/16073606.2022.2112629
F. J. H. Don, “On the symmetric solutions of a linear matrix equation,” Linear Algebra Appl., 93, 1–7 (1987), https://doi.org/10.1016/S0024-3795(87)90308-9
O. Helmer, “The elementary divisor theorem for certain rings without chain conditions,” Bull. Amer. Math. Soc., 49, No. 4, 225–236 (1943), https://doi.org/10.1090/S0002-9904-1943-07886-X
I. Kaplansky, “Elementary divisors and modules,” Trans. Amer. Math. Soc., 66, No. 2, 464–491 (1949), https://doi.org/10.1090/S0002-9947-1949-0031470-3
C. G. Khatri, S. K. Mitra, “Hermitian and nonnegative definite solutions of linear matrix equations,” SIAM J. Appl. Math., 31, No. 4, 579–585 (1976), https://doi.org/10.1137/0131050
J. R. Magnus, “L-structured matrices and linear matrix equations,” Linear Algebra Appl., 14, No. 1, 67–88 (1983), https://doi.org/10.1080/03081088308817543
J. R. Magnus, H. Neudecker, “The elimination matrix: Some lemmas and applications,” SIAM J. Algebraic Discrete Methods, 1, No. 4, 422–449 (1980), https://doi.org/10.1137/0601049
A. C. M. Ran, M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proc. Amer. Math. Soc., 132, No. 5, 1435–1443 (2004), https://doi.org/10.1090/S0002-9939-03-07220-4
B. Recht, M. Fazel, P. A. Parrilo, “Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,” SIAM Review, 52, No. 3 (2010), https://doi.org/10.1137/070697835
V. Shchedryk, “Arithmetic of matrices over rings,” Akademperiodyka, Kyiv (2021), https://doi.org/10.15407/akademperiodika.430.278
W. J. Vetter, “Vector structures and solutions of linear matrix equations,” Linear Algebra Appl., 10, No. 2, 181–188 (1975), https://doi.org/10.1016/0024-3795(75)90010-5
Посилання
- Поки немає зовнішніх посилань.
Ця робота ліцензована Creative Commons Attribution 3.0 License.