Различия
Показаны различия между двумя версиями страницы.
| Предыдущая версия справа и слева Предыдущая версия Следующая версия | Предыдущая версия | ||
| math:t2-04 [2022/03/28 06:02] – root | math:t2-04 [2023/03/12 15:06] (текущий) – [Построение функции от матрицы без нахождения матрицы преобразования] root | ||
|---|---|---|---|
| Строка 115: | Строка 115: | ||
| 5 & -7 & 3\\ | 5 & -7 & 3\\ | ||
| 1 & -2 & 1 | 1 & -2 & 1 | ||
| - | \end{array}\right)\underset{\to}{(2)-5(3)}\left(\begin{array}{ccc} | + | \end{array}\right)\underset{\to}{(2)-5(3)} |
| + | $$ | ||
| + | $$ | ||
| + | \left(\begin{array}{ccc} | ||
| 0 & 3 & -2\\ | 0 & 3 & -2\\ | ||
| 0 & 3 & -2\\ | 0 & 3 & -2\\ | ||
| Строка 155: | Строка 158: | ||
| 0 & 1 & 0\\ | 0 & 1 & 0\\ | ||
| 0 & 1 & 1 | 0 & 1 & 1 | ||
| - | \end{array}\right)\underset{\to}{(1)-2(3)}\left(\begin{array}{ccc} | + | \end{array}\right)\underset{\to}{(1)-2(3)} |
| + | $$ | ||
| + | $$ | ||
| + | \left(\begin{array}{ccc} | ||
| -1 & 0 & 2\\ | -1 & 0 & 2\\ | ||
| -1 & 0 & 3\\ | -1 & 0 & 3\\ | ||
| Строка 220: | Строка 226: | ||
| 0 & 2^{4} & 0\\ | 0 & 2^{4} & 0\\ | ||
| 0 & 0 & 3^{4} | 0 & 0 & 3^{4} | ||
| - | \end{array}\right)T^{-1}=\left(\begin{array}{ccc} | + | \end{array}\right)T^{-1}= |
| + | $$ | ||
| + | $$ | ||
| + | \left(\begin{array}{ccc} | ||
| 1 & 0 & 1\\ | 1 & 0 & 1\\ | ||
| 2 & 1 & 1\\ | 2 & 1 & 1\\ | ||
| Строка 267: | Строка 276: | ||
| 0 & e^{2} & 0\\ | 0 & e^{2} & 0\\ | ||
| 0 & 0 & e^{3} | 0 & 0 & e^{3} | ||
| - | \end{array}\right)T^{-1}=\left(\begin{array}{ccc} | + | \end{array}\right)T^{-1}= |
| + | $$ | ||
| + | $$ | ||
| + | \left(\begin{array}{ccc} | ||
| 1 & 0 & 1\\ | 1 & 0 & 1\\ | ||
| 2 & 1 & 1\\ | 2 & 1 & 1\\ | ||
| Строка 508: | Строка 520: | ||
| 0 & 1 & 2t\lambda_{1} & f^{(1)}\left(t\lambda_{1}\right)\\ | 0 & 1 & 2t\lambda_{1} & f^{(1)}\left(t\lambda_{1}\right)\\ | ||
| 1 & t\lambda_{3} & t^{2}\lambda_{3}^{2} & f\left(t\lambda_{3}\right) | 1 & t\lambda_{3} & t^{2}\lambda_{3}^{2} & f\left(t\lambda_{3}\right) | ||
| - | \end{array}\right|=t\cdot t^{2}\left|\begin{array}{cccc} | + | \end{array}\right|= |
| + | t\cdot t^{2}\left|\begin{array}{cccc} | ||
| E & A & A^{2} & f\left(tA\right)\\ | E & A & A^{2} & f\left(tA\right)\\ | ||
| - | 1 & \lambda_{1} & t^{2}\lambda_{1}^{2} & f\left(t\lambda_{1}\right)\\ | + | 1 & \lambda_{1} & \lambda_{1}^{2} & f\left(t\lambda_{1}\right)\\ |
| 0 & t^{-1} & 2t^{-1}\lambda_{1} & f^{(1)}\left(t\lambda_{1}\right)\\ | 0 & t^{-1} & 2t^{-1}\lambda_{1} & f^{(1)}\left(t\lambda_{1}\right)\\ | ||
| 1 & \lambda_{3} & \lambda_{3}^{2} & f\left(t\lambda_{3}\right) | 1 & \lambda_{3} & \lambda_{3}^{2} & f\left(t\lambda_{3}\right) | ||
| - | \end{array}\right|=$$ | + | \end{array}\right| |
| + | $$ | ||
| + | следовательно | ||
| $$ | $$ | ||
| \left|\begin{array}{cccc} | \left|\begin{array}{cccc} | ||
| E & A & A^{2} & f\left(tA\right)\\ | E & A & A^{2} & f\left(tA\right)\\ | ||
| - | 1 & \lambda_{1} & t^{2}\lambda_{1}^{2} & f\left(t\lambda_{1}\right)\\ | + | 1 & \lambda_{1} & \lambda_{1}^{2} & f\left(t\lambda_{1}\right)\\ |
| 0 & 1 & 2\lambda_{1} & tf^{(1)}\left(t\lambda_{1}\right)\\ | 0 & 1 & 2\lambda_{1} & tf^{(1)}\left(t\lambda_{1}\right)\\ | ||
| 1 & \lambda_{3} & \lambda_{3}^{2} & f\left(t\lambda_{3}\right) | 1 & \lambda_{3} & \lambda_{3}^{2} & f\left(t\lambda_{3}\right) | ||
| \end{array}\right|=0.$$ | \end{array}\right|=0.$$ | ||