1. Not finding help here? Sign up for a free 30min 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!

E^At problem

  1. Mar 30, 2008 #1
    e^At problem!!

    1. The problem statement, all variables and given/known data[/b]

    Hi
    for given 4 by 4 matrix, say A, find the e[tex]^{At}[/tex]
    which t is time variable.


    2. Relevant equations

    [tex]A= {\left(\begin{array}{cccc} 0 & a & 0 & 0 \\ -a& 0 & 0 & 0\\ 0 & 0 & 0 & a\\0 & 0 & -a & 0 \end{array}\right)t}Y(0)[/tex].


    3. The attempt at a solution
     
    Last edited by a moderator: Mar 30, 2008
  2. jcsd
  3. Mar 30, 2008 #2
    ............................
     
  4. Mar 30, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The Latex should be

    [tex]A= {\left(\begin{array}{cccc} 0 & a & 0 & 0 \\ -a& 0 & 0 & 0\\ 0 & 0 & 0 & a\\0 & 0 & -a & 0 \end{array}\right)t}Y(0)[/tex]
    You forgot the ending "[ / tex ]" and, the reason it didn't show up right when I edited your post and in sutupidmath's post is because you also have "{cc}" rather than the "{cccc}" you need for 4 columns.

    Now, what have you done about this problem your self? This can be written as a "block" matrix of the form
    [tex]\left(\begin{array}{cc}A & 0 \\ 0 & A\end{array}\right)[/tex]
    where
    [tex]A= \left(\begin{array}{cc}0 & a \\ -a & 0\end{array}\right)[/tex]
    so it should be easy to find a general formula for the powers of the matrix and then use the Taylor's series for ex.
     
    Last edited: Mar 30, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: E^At problem
  1. The number e (Replies: 6)

Loading...