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!

Exponential matrix problem and Putzer's formula

  1. Jun 18, 2011 #1
    1. The problem statement, all variables and given/known data

    [itex]e^{ \begin{bmatrix} \lambda_{1} & 0 \\ 1& \lambda_{2} \end{bmatrix}t } [/itex]=\begin{bmatrix} e^{\lambda_{1}t} & 0 \\
    \frac{e^{\lambda_{2}t} - e^{\lambda_{1}t}}{ \lambda_{2} - \lambda_{1}} & e^{\lambda_{2}t}
    \end{bmatrix}

    with [itex]\lambda_{1}\neq \lambda_{2}[/itex]
    2. Relevant equations

    Could someone solve this for me?

    3. The attempt at a solution

    I am no good at maths... with basic knowledge of linear algebra.
    It looks like [itex]\lambda_{1} , \lambda_{2}[/itex] are the eigenvalues of a matrix A that solves a differential system. All indications are pointing to Putzer's formula, but everything i have tried failed. Probably i am missing something....

    Thanks in advance...
    p.s.Sorry for my terrible English
     
  2. jcsd
  3. Jun 18, 2011 #2

    hunt_mat

    User Avatar
    Homework Helper

    Basically you write out the definition of the exponential:
    [tex]
    e^{x}=1+x+\frac{x^{2}}{2!}+\cdots +\frac{x^{n}}{n!}+\cdots
    [/tex]
    To compute the LHS of your equation, you will have you figure out an equation for:
    [tex]
    \left(
    \begin{array}{cc}
    \lambda_{1} & 0 \\
    1 & \lambda_{2}
    \end{array}\right)^{n}
    [/tex]
    and this will give you what you require.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Exponential matrix problem and Putzer's formula
  1. Matrix exponential (Replies: 4)

  2. Matrix exponential (Replies: 4)

  3. Matrix Exponentials (Replies: 2)

Loading...