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Adjoint of an equation

  1. Oct 12, 2012 #1
    This is not a homework problem, just trying to figure out what shankar did.
    [itex] U|u_i>=u_i|u_i> [/itex]
    [itex] U|u_j>=u_j|u_j> [/itex]
    Ok so we have these 2 equations and then shankars says to take the adjoint
    of the second equation and dot each side with the corresponding side of the first equation,
    we get
    [itex] <u_j|U^tU|u_i=u_i{u_j}^*<u_j|u_i> [/itex]
    is the [itex] {u_j}^* [/itex] just the complex conjugate of [itex] u_j [/itex] ?
    Now that I typed it out it seems more clear I originally thought there was an extra factor.
  2. jcsd
  3. Oct 13, 2012 #2
    Yes, u* is the complex conjugate of u.
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