Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Complex conjugate of a 5 x 5 matrices?
Loading...