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E^At problem

  • Thread starter jahandideh
  • Start date
e^At problem!!

1. Homework Statement [/b]

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


2. Homework 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
 
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Answers and Replies

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4
1. Homework Statement [/b]

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


2. Homework Equations

[tex]A= {\left(\begin{array}{cc} 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
............................
 
HallsofIvy
Science Advisor
Homework Helper
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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.
 
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