Problem A.18 - Exploring the Eigen landscape ⇢ Eigenvalues and Eigenvectors: Intro to QM Appendix

⍟ 𝐀𝐛𝐨𝐮𝐭 𝐓𝐡𝐢𝐬 𝐕𝐢𝐝𝐞𝐨 ⍟
Explore the fascinating world of eigenvalues and eigenvectors, essential concepts in linear algebra that unlock the secrets of rotational dynamics. In this video, we explore how these mathematical tools apply to 2D rotation matrices, revealing their complex eigenvalues and the special cases where they become real. Discover the significance of these concepts in various fields, from engineering to quantum physics, and learn how to diagonalize matrices through similarity transformations. Join us as we decode the equations that govern these mathematical marvels and see how they shape our understanding of the universe!

• 𝙿𝚛𝚘𝚋𝚕𝚎𝚖 𝙱𝚛𝚎𝚊𝚔𝚍𝚘𝚠𝚗 𝚃𝚒𝚖𝚎 𝚂𝚝𝚊𝚖𝚙𝚜:
00:00 - Intro & Background.
00:31 - Problem Statement.
02:36 - Eigenvalues.
07:42 - Eigenvectors.
17:29 - Diagonalization.
23:14 - Concluding Remarks.
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⍟ 𝐂𝐫𝐞𝐝𝐢𝐭𝐬/𝐑𝐞𝐬𝐨𝐮𝐫𝐜𝐞𝐬 ⍟
☞📚📖📓= Griffiths, David J., and Darrell F. Schroeter. “Appendix: Linear Algebra.” 𝘐𝘯𝘵𝘳𝘰𝘥𝘶𝘤𝘵𝘪𝘰𝘯 𝘵𝘰 𝘘𝘶𝘢𝘯𝘵𝘶𝘮 𝘔𝘦𝘤𝘩𝘢𝘯𝘪𝘤𝘴, 3rd ed., Cambridge University Press, 2018, pp. 464–485.

• https://sciencethedata.com/2022/02/19...
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Science is a phenomenal exploration of nature. We hope to hone our skills of problem solving by exposing ourselves to multiple contexts. In doing so, it can sometimes be challenging to see the connection between topics. I yearn to understand 𝙝𝙤𝙬 these aspects of physics, unite together. To accomplish this, I'll cover all of my old textbooks through QFT; the convergence point of the many modern scientists! These posts are very much in a "𝘯𝘰𝘵𝘦𝘴 𝘵𝘰 𝘴𝘦𝘭𝘧" style. 𝙈𝙮 𝙝𝙤𝙥𝙚 is that by sharing this exploration, I can help others navigate the beautiful world of mathematics & physics through problems and examples, connecting the mathematical tools to their physical ramifications.

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