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Heisenberg's Uncertainty Principle using Linear Algebra

  1. Jan 7, 2015 #1
    I am working through linear algebra from MITs MOOC online courses. One of the question refers to the uncertainty principle. It states:

    AB-BA=I can happen for infinite matrices with A

    [tex]A=A^{ T }\\ and\\ B=-B^{ T }\\ Then\\ x^{ T }x=x^{ T }ABx-x^{ T }BAx\le 2\parallel Ax\parallel \parallel Bx\parallel[/tex]

    My question is how does
    [tex]x^{ T }x=x^{ T }ABx-x^{ T }BAx [/tex]?
  2. jcsd
  3. Jan 7, 2015 #2


    Staff: Mentor

    Like you said:
  4. Jan 8, 2015 #3
    Okay. I should have got that one. :) Okay, now I want to prove the premise AB-BA=I, is there an elegant way of doing that?
  5. Jan 8, 2015 #4


    Staff: Mentor

    That is the premise of the theorem except for a multiplicative constant - the I is replaced by iC - C a real constant.

  6. Jan 11, 2015 #5
    Thanks again I really appreciate your attention.
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