Надіслати цю статтю Про розв’язки матричного рівняння AX+YB=C над кільцем цілих чисел
Анотація
Досліджено розв’язність матричного рівняння типу Сильвестра AX+YB=C над кільцем цілих чисел $\mathbb{Z}$. Встановлено класи сумісних матричних рівнянь типу Сильвестра над $\mathbb{Z}$ та описано структуру їхніх розв'язків. Якщо A та B є неособливими матрицями із взаємно простими визначниками, запропоновано метод побудови розв’язку цього рівняння та встановлено умови його єдиності. Крім того, наведено умови, за яких рівняння типу Сильвестра AX+YB=C над $\mathbb{Z}$ має єдиний «мінімальний» розв'язок, тобто такий, на який накладено певні обмеження.
Зразок для цитування: В. М. Прокіп, “Про розв’язки матричного рівняння AX+YB=C над кільцем цілих чисел”, Мат. методи та фіз.-мех. поля, 68, No. 1-2, 28–38 (2025), https://doi.org/10.15407/mmpmf2025.68.1-2.28-38
Ключові слова
Посилання
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