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Вот что даёт в ответ эта страница в Интернет-сети (чтобы её воспроизвести, Вам нужно "кликнуть" по ссылке и в открывшемся в браузере окне установить размеры матрицы, и ввести элементы её ячеек согласно условию):
Перечислим собственные значения и собственные вектора матрицы A = [0 1 0 0] [0 0 1 0] [0 0 0 1] [1 0 0 0] : Собственное значение l1 = (-1+0j). Собственный вектор v1 = [-0.5+0.j] [ 0.5+0.j] [-0.5+0.j] [ 0.5+0.j]; Собственное значение l2 = (-1.60190870985e-17+1j). Собственный вектор v2 = [ -5.00000000e-01 +7.99192526e-17j] [ 1.55989588e-17 -5.00000000e-01j] [ 5.00000000e-01 +0.00000000e+00j] [ -6.88739430e-17 +5.00000000e-01j]; Собственное значение l3 = (-1.60190870985e-17-1j). Собственный вектор v3 = [ -5.00000000e-01 -7.99192526e-17j] [ 1.55989588e-17 +5.00000000e-01j] [ 5.00000000e-01 +0.00000000e+00j] [ -6.88739430e-17 -5.00000000e-01j]; Собственное значение l4 = (1+0j). Собственный вектор v4 = [-0.5+0.j] [-0.5+0.j] [-0.5+0.j] [-0.5+0.j].
Если одно из чисел близко к нулю, то это скорее всего 0, если Вы конечно не работаете с близкими к 0 числами.
Как видно, в области действительных чисел заданная матрица имеет два собственных значения и соответствующих им собственных вектора. Найдём теперь их самостоятельно, помня об имеющейся подсказке.
Полученный результат отличается от "подсказанного" только формой представления.
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