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A positive definite Hermitian Form

  1. Oct 26, 2004 #1
    In this question I let "x1t , x2t, x3t " be the conjugate of x1, x2, x3

    The hermitian form
    Hc(x) = c*x1t*x1 + 2*x2t*x2 - i*x1t*x2 + i*x2t*x1 + x1t*x3 + x3t*x1
    +i*x2t*x3 - i*x3t*x2 (sorry, it`s a bit messy)

    For which value of c is Hc ositive definite?

    I have tried to find the eignvalue in terms of c by trying to solve the
    charactiristic polynomial, but seems too complicate to do, I`ve also tried
    to solve by completing the square but not so successful.
    So is there any way to solve this without using computer softwares like
    maple? Thanks
  2. jcsd
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