1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

General Form of 3x3 unitary matrix

  1. Feb 9, 2008 #1

    Does anyone know the general form of a 3x3 Unitary Matrix? I know for 2x2 it can be parametrized by 2 complex numbers. I remember once seeing a general form for the 3x3 in terms of 6, I think, complex numbers. Anyway, I'm having trouble finding that now...so if anyone could help me it would be greatly appreciated.

  2. jcsd
  3. Feb 9, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    I'm not sure if this is what you mean, but any nxn unitary matrix is similar to a matrix of the form

    [tex]\left(\begin{array}{ccc} e^{i \theta_1} & & 0 \\ & \ddots & \\ 0 & & e^{i \theta_n} \end{array}\right)[/tex]

    This is because a unitary matrix is diagonalizable and its eigenvalues all lie on the unit circle (i.e. have absolute value 1).
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: General Form of 3x3 unitary matrix