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Консультация № 201222
26.06.2021, 21:45
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Здравствуйте! У меня возникли сложности с таким вопросом:
Пусть (е1,е2)-ортонормированный базис евклидового пространства и оператор фи имеет матрицу А в базисе (e'1,e'2).Найти матрицу сопряженного оператора в этом базисе,если A=<(2,-1),(-4,3)>,(e'1,e'2)=(3e1+2e2,-2e1-e2)
Пусть (е1,е2)-ортонормированный базис евклидового пространства и оператор фи имеет матрицу А в базисе (e'1,e'2).Найти матрицу сопряженного оператора в этом базисе,если A=<(2,-1),(-4,3)>,(e'1,e'2)=(3e1+2e2,-2e1-e2)
Обсуждение
28.06.2021, 08:13
общий
это ответ
Здравствуйте, Logan_Lady!
Согласно условию задачи, оператор
имеет матрицу
в базисе
причём координаты векторов
заданы в ортонормированном базисе 
Вычислим скалярные произведения и составим матрицу Грама:
Определим матрицу
сопряжённого оператора в базисе 
(чтобы избежать ошибок при вычислениях вручную, был использован этот онлайн-калькулятор: Ссылка >>).
Решим предложенную задачу другим способом. Матрица
является матрицей перехода от ортонормированного базиса
в котором были заданы координаты векторов к базису из этих векторов. Определим матрицу 
оператора в ортонормированном базисе:
Определим матрицу
сопряжённого оператора в ортонормированном базисе:
Определим матрицу сопряжённого оператора в базисе
При решении задачи я использовал формулы отсюда: Ссылка >>.
Согласно условию задачи, оператор
имеет матрицув базисе
причём координаты векторов
заданы в ортонормированном базисе Вычислим скалярные произведения и составим матрицу Грама:
Определим матрицу
сопряжённого оператора в базисе (чтобы избежать ошибок при вычислениях вручную, был использован этот онлайн-калькулятор: Ссылка >>).
Решим предложенную задачу другим способом. Матрица
является матрицей перехода от ортонормированного базиса
в котором были заданы координаты векторов к базису из этих векторов. Определим матрицу оператора в ортонормированном базисе:Определим матрицу
сопряжённого оператора в ортонормированном базисе:Определим матрицу
сопряжённого оператора в базисе При решении задачи я использовал формулы отсюда: Ссылка >>.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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