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Hermitian Matrix

  1. May 22, 2014 #1
    Hello,

    If I have a Hermitian matrix A, can I write it as:

    [tex]\mathbf{A}=\mathbf{A}^{1/2}\mathbf{A}^{H/2}[/tex]

    where superscript H denotes hermitian operation?

    Thanks
     
  2. jcsd
  3. May 22, 2014 #2
    What do you mean with ##H/2##? Do you mean

    [tex](A^H)^{1/2}[/tex]

    or something similar?
     
  4. May 22, 2014 #3
    Yes exactly, it means the square root of the complex conjugation transpose of A.
     
  5. May 22, 2014 #4
    OK, but if ##A## is hermitian, then ##A^H = A##, no? So you can write your original post as

    [tex]A = A^{1/2}A^{1/2}[/tex]

    which is certainly true.
     
  6. May 22, 2014 #5
    Oh, I didn't see it that way. Thanks
     
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