Thread: Lyapunov equation

Hello...I searched very much on the web... examples for matrices A and C for the Lyapunov equation:

A* X + X * A' = C

do u have any suggestion?


thank you

Hello Inzaghina! If examples are all your looking for then the most trivial and easiest to find are to either set $\displaystyle A = I$ , the Identity matrix, or $\displaystyle X = I $. In the first case then you have that

$\displaystyle 2X = C$

so choose any arbitrary X matrix and the $\displaystyle C$ is given by the above. In the second case you have that

$\displaystyle A + A^T = C$

so this time pick any matrix for A and then use the above to give you an example of $\displaystyle C$.

I have met this beast before but have to say that in my experience it's usually the case that you know $\displaystyle A $ and $\displaystyle C$ and need to find $\displaystyle X$!