Functional Analysis 34 | Spectral Theorem for Compact Operators

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  • เผยแพร่เมื่อ 25 ธ.ค. 2024

ความคิดเห็น • 13

  • @brightsideofmaths
    @brightsideofmaths  ปีที่แล้ว +4

    New upload because I corrected a small typo :)

    • @elsa1569
      @elsa1569 ปีที่แล้ว

      Thank you. Looking forward to the next video with examples and applications 😊

  • @Hopegood7031
    @Hopegood7031 หลายเดือนก่อน

    Hello Sir, I appreciate your efforts to make these excellent, high-level videos to teach others and share your knowledge. Lately, I've discovered your channel, and it helps me organize my understanding of math for my PhD research in quantum computing. I wanted to learn the math basics, and this serie is one of your other series that makes the mathematical concepts clear.

    • @brightsideofmaths
      @brightsideofmaths  หลายเดือนก่อน

      Thank you very much :) And thanks for your support!

  • @Magistrixification
    @Magistrixification ปีที่แล้ว +5

    Something is tickling my brain from my physics degree 13 years ago. Quantum theory?

  • @yoyostutoring
    @yoyostutoring ปีที่แล้ว

    Consider V=C (set of complex numbers), which is a C-vector space, and if T:C -> C defined by Tz = 0, for all z, then T is a linear, bounded, compact, and a self-adjoint operator, but the norm of the operator is 0 which implies that the eigenvalues must be zero. However, these lambdas are not in C\{0}. What am I doing wrong?

    • @yoyostutoring
      @yoyostutoring ปีที่แล้ว

      By the way, inner product is standard inner product for C.

    • @brightsideofmaths
      @brightsideofmaths  ปีที่แล้ว +1

      @@yoyostutoring Everything is good. What exactly is your problem there?

    • @yoyostutoring
      @yoyostutoring ปีที่แล้ว

      There is a "contradiction" which is about the lambdas I talked about earlier in the comment above.

    • @brightsideofmaths
      @brightsideofmaths  ปีที่แล้ว +2

      I is empty :)

    • @yoyostutoring
      @yoyostutoring ปีที่แล้ว

      @brightsideofmaths Now this solved the problem! Lmao 🤣 thanks!

  • @iharsh386
    @iharsh386 10 หลายเดือนก่อน

    is the series ended?

    • @brightsideofmaths
      @brightsideofmaths  10 หลายเดือนก่อน +2

      Not really. It continuous with unbounded operators: tbsom.de/s/uo