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

Exponential of a Matrix

  1. Jul 24, 2009 #1
    Will anyone help me to find out the analytic expression
    of the following [tex]2^N\times2^N[/tex] exponential?

    [tex]exp[t(X\otimes X\otimes I\ldots\otimes I+I\otimes X\otimes X\otimes I\ldots\otimes I+\ldots+I\otimes I\otimes\ldots I \otimes X \otimes X+X\otimes I\ldots I\otimes X)][/tex],


    I= \left[\begin{array}{cc}
    1 & 0 \\
    0 & 1 \end{array}\right] [/tex]

    0 & 1 \\
    1 & 0 \end{array}\right]


    [Note that the parenthesis in the `exponential' contains sum of N+1 terms each of which is a tensor product of 2 Xs and (N-2) of Is in some order.]

    I've evaluated (via Mathematica) for N=3,4,5,6. But I need an analytic expression for it.

    Thanks and Regards.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted