Create: 2025-02-28 Update: 2025-07-10 12:38:16

QR алгоритм

🥸 Одна из жемчужин численных методов. Он используется для поиска собственных чисел матрицы.

🥰 Простой и стабильный, а при небольших модификациях ещё и быстрый.

Qₖ, Rₖ = qr(Aₖ) - Вычисляем QR-разложение матрицы
Aₖ₊₁ = RₖQₖ - Умножаем факторы в обратном порядке

😑 Для произвольной квадратной матрицы он сходится к верхнетреугольной матрице, на диагонали которой стоят её собственные числа (картинка слева)

👍 Если же матрица - симметричная, то он сходится вообще к диагональной матрице собственных чисел (картинка справа).

Идея анимации взята у Gabriel Peyré - один из лучших аккаунтов по красивым математическим визуализациям. По моим предварительным исследованиям, после этого поста отпишется наибольшее количество уважаемых подписчиков.👌

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Telegram Desktop App Not Working on Windows?

Run Telegram in Compatibility Mode

The fix won't work if the app was functioning normally a few days ago and you haven't made drastic changes to the OS or updated Windows. If the issue appears after a Windows update, or you're running an older version of Telegram, it's possible the current version of the app isn't compatible with your operating system. Therefore, update your app to the most recent and compatible version or roll back your Windows update.If you can't do either, run the app in compatibility mode. You might not have used it before, but it is one of the handy hidden modes in Windows.However, before doing that, run the compatibility troubleshooter that may resolve the issue right away. To run the troubleshooter, right-click on Telegram's shortcut and go to Properties. Navigate to the Compatibility tab in the Telegram Properties window and click Run compatibility troubleshooter.If the troubleshooter doesn't identify the issue, manually adjust compatibility settings. To do so, follow these steps: Check the box for Run this problem in compatibility mode for: and select Windows 8 from the dropdown menu. Hit OK after clicking Apply.

QR алгоритм

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