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Complex conjugate of a 5 x 5 matrices?

  1. Jun 2, 2005 #1
    How do you do it?
     
  2. jcsd
  3. Jun 3, 2005 #2

    matt grime

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    To get the complex conjugate of any matrix you just conjugate each entry.
     
  4. Jun 6, 2005 #3
    Sorry im doing something similar; converting a ket into a bra. wouldn't something change like order.
     
    Last edited: Jun 6, 2005
  5. Jun 6, 2005 #4

    HallsofIvy

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    matt grime is completely right for "complex conjugate". However, you may be intending "Hermitian conjugate" or "adjoint". To find the Hermitian conjugate (adjoint) of a complex matrix you take the complex conjugate of each entry and take the transpose: rows become columns.
     
  6. Jun 6, 2005 #5
    Can i get a 5*5 matrices example
     
  7. Jun 7, 2005 #6
    [tex]A = \left(\begin{array}{ccccc}0 & i & 3 & 2 & 1 - 2i \\ -i & 7 & 6 & 4 & 0 \\
    3 + i & 2 & 0 & -2i & 4 \\ 9 & 1 & i & 8 & 1 \\ 0 & 0 & 0 & 7i & 0\end{array}\right)[/tex] [tex]A^T = \left(\begin{array}{ccccc}0 & -i & 3 + i & 9 & 0 \\ i & 7 & 2 & 1 & 0 \\ 3 & 6 & 0 & i & 0 \\ 2 & 4 & -2i & 8 & 7i \\ 1 - 2i & 0 & 4 & 1 & 0\end{array}\right)[/tex] [tex]A^\dagger = \left(\begin{array}{ccccc}0 & i & 3 - i & 9 & 0 \\ -i & 7 & 2 & 1 & 0 \\ 3 & 6 & 0 & -i & 0 \\ 2 & 4 & 2i & 8 & -7i \\ 1 + 2i & 0 & 4 & 1 & 0\end{array}\right)[/tex]

    I hope that's right and I've not made any mistakes.
     
  8. Jun 7, 2005 #7

    HallsofIvy

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    In Nylex's example, [tex]A^T[/tex] is the transpose and [tex]A^{\dagger}[/tex] is the Hermitian conjugate or adjoint.
    Using the same example, the "complex conjugate" that was originally asked for, and matt grimes described, would be
    [tex]A^* = \left(\begin{array}{ccccc}0 & -i & 3 & 2 & 1 + 2i \\ i & 7 & 6 & 4 & 0 \\3 - i & 2 & 0 & 2i & 4 \\ 9 & 1 & -i & 8 & 1 \\ 0 & 0 & 0 & -7i & 0\end{array}\right)[/tex]
     
  9. Jun 10, 2005 #8
    nice examples
     
    Last edited: Jun 10, 2005
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