Heisenberg's Uncertainty Principle using Linear Algebra

  • Thread starter rpthomps
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  • #1
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Main Question or Discussion Point

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]?
 

Answers and Replies

  • #2
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  • #3
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Like you said:


Thanks
Bill
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?
 
  • #4
9,331
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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?
That is the premise of the theorem except for a multiplicative constant - the I is replaced by iC - C a real constant.

Thanks
Bill
 
  • #5
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Thanks again I really appreciate your attention.
 

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