What is the e^At Problem for a 4x4 Matrix?

[jahandideh]

e^At problem!

1. Homework Statement [/b]

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

Homework Equations

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

The Attempt at a Solution

 

[sutupidmath]

1. Homework Statement [/b]

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

Homework Equations

$$A= {\left(\begin{array}{cc} 0 & a & 0 & 0 \\ -a& 0 & 0 & 0\\ 0 & 0 & 0 & a\\0 & 0 & -a & 0 \end{array}\right)t}Y(0)$$.

The Attempt at a Solution

......

 

[HallsofIvy]

The Latex should be

$$A= {\left(\begin{array}{cccc} 0 & a & 0 & 0 \\ -a& 0 & 0 & 0\\ 0 & 0 & 0 & a\\0 & 0 & -a & 0 \end{array}\right)t}Y(0)$$
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
$$\left(\begin{array}{cc}A & 0 \\ 0 & A\end{array}\right)$$
where
$$A= \left(\begin{array}{cc}0 & a \\ -a & 0\end{array}\right)$$
so it should be easy to find a general formula for the powers of the matrix and then use the Taylor's series for e^x.