>LTI square system represented in state space form
>change the order in which the equations are written
>thus the rows of the matrix A are rearranged
>the eigenvalues change values
>stable systems can become unstable by writting the equations in a different order
This doesn't make any fucking sense. Math is a flawed tool for modelling real systems. Everything you believe is a lie.
Or you're too much of a brainlet to use it correctly
>Interchanging rows changes eigenvalues
BRAINLET
I already stated the facts. It doesn't make sense that writting equations in a different order affects the system stability and response speed. You're so blind by your faith in math that you can't face the truth.
Pic related.
Changing rows of a matrix =/= changing order of the equation brainlet.
LOL
Now calculate them by hand both ways and read the documentation for the eig() function. You fucking brainlet.
it does though, consider the identity matrix vs [0 1; 1 0]
Then explain pic related (J is the jacobian matrix of the system and E.E. is the steady state solution).
What are you talking about? The eig() function returns the eigenvalues of the matrix. Calculate them by hand yourself if doubt. But if you are too lazy, consider the 2x2 system in pic related.
It's meaningless call me a brainlet if neither of you can prove me wrong.
>inb4 it should be the square root of alpha times beta in the first case
I know. My point still stands though.
Fug :D
But OP is a brainlet regardless. If you're interchanging the rows, you should interchange the columns as well. The matrix [math] A [/math] becomes [math] PAP^T [/math], so the eigenvalues don't change.