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Homework Help: Algebraic Problem

  1. Nov 29, 2004 #1
    I need help proving this equation... Thankful for all answers!

    [tex]
    \tilde{(\hat{A} +
    \hat{B})^*} =
    \tilde{\hat{A}}^* +
    \tilde{\hat{B}}^*
    [/tex]

    I hope you can read my nice Latex equation! :)
     
  2. jcsd
  3. Nov 29, 2004 #2

    dextercioby

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    Explain what everything means:tilda stands for what?star stands for what?hats stand for what??
    P.S.I had my glasses on,so i could read it. :wink:
     
  4. Nov 29, 2004 #3

    arildno

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    I would assume it is about (complex) conjugates and transposes, but I'm not sure..
     
  5. Nov 29, 2004 #4
    at think the same thing arildno...and since these operations are per definition linear there is not much to say...

    regards
    marlon
     
  6. Nov 29, 2004 #5

    dextercioby

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    The problem is not that simple.In general,linear operators can be bounded/unbounded.So the general formula reads.
    [tex] (\hat{A} +\hat{B})^{+} \supseteq \hat{A}^{+}+\hat{B}^{+} [/tex]
    ,where the sign for operator equality stands for bounded linear operators A and B.
     
  7. Nov 29, 2004 #6
    My latex knowledge ís not that good... but dextercioby wrote my problem down for me except that there is an equality sign in my problem! What i want to do is to prove equality. I cant just say that the operators are linear and write the answer down.

    Please... some advice!
     
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