Arbitrary operator as a sum of Hermitian operators

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Probaly already asked.




Show that an arbitrary operator $A$ can be written as $A=B+iC$, where $B$ and $C$ are Hermitian.




I think the matrix version is the sum of a symmetric and antisymmetry part, but I have no idea how to do it in the general case.







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    up vote
    0
    down vote

    favorite












    Probaly already asked.




    Show that an arbitrary operator $A$ can be written as $A=B+iC$, where $B$ and $C$ are Hermitian.




    I think the matrix version is the sum of a symmetric and antisymmetry part, but I have no idea how to do it in the general case.







    share|cite|improve this question






















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Probaly already asked.




      Show that an arbitrary operator $A$ can be written as $A=B+iC$, where $B$ and $C$ are Hermitian.




      I think the matrix version is the sum of a symmetric and antisymmetry part, but I have no idea how to do it in the general case.







      share|cite|improve this question












      Probaly already asked.




      Show that an arbitrary operator $A$ can be written as $A=B+iC$, where $B$ and $C$ are Hermitian.




      I think the matrix version is the sum of a symmetric and antisymmetry part, but I have no idea how to do it in the general case.









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 10 at 20:09









      user2820579

      678412




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          Hint




          $$B=fracA+A^*2;;;;;C=fracA-A^*2i$$







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          1 Answer
          1






          active

          oldest

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          active

          oldest

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          active

          oldest

          votes








          up vote
          1
          down vote



          accepted










          Hint




          $$B=fracA+A^*2;;;;;C=fracA-A^*2i$$







          share|cite|improve this answer
















          • 1




            I want my entrance fee back.
            – user2820579
            Aug 10 at 20:55














          up vote
          1
          down vote



          accepted










          Hint




          $$B=fracA+A^*2;;;;;C=fracA-A^*2i$$







          share|cite|improve this answer
















          • 1




            I want my entrance fee back.
            – user2820579
            Aug 10 at 20:55












          up vote
          1
          down vote



          accepted







          up vote
          1
          down vote



          accepted






          Hint




          $$B=fracA+A^*2;;;;;C=fracA-A^*2i$$







          share|cite|improve this answer












          Hint




          $$B=fracA+A^*2;;;;;C=fracA-A^*2i$$








          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 10 at 20:12









          Davide Morgante

          2,245322




          2,245322







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            I want my entrance fee back.
            – user2820579
            Aug 10 at 20:55







          1




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          – user2820579
          Aug 10 at 20:55




          I want my entrance fee back.
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