>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.
>real systems
HAHAHAHAHAHAHAHAHAHAHA
>Math is a flawed tool for modelling real systems.
So you found one example of something (which you're probably misinterpreting). If anything, it sheds light on the incompetence of those who tried to apply it.
I imagine the applied mathematicians and engineers thinking about this stuff thought about this sort of thing. Go ask an expert about it and you'll get a sensible answer.
See the Lotka-Volterra example above. Explain to me why it should matter which term comes first in a sum or which equation is written first.
Alternatively, suppose I'm modelling a chemical reactor, why it should matter if I do a mass balance for component B before component A? Why it should matter if I write the the generation term before the input/output mass terms?
I'm not questioning your math detached from reality, I'm questioning it's application to real problems.
>Go ask an expert about it and you'll get a sensible answer.
I would if I could.
It appears you don't understand what is actually a Jacobian matrix. You just make sure you copy dumbly what's in your book.
So. Start from scratch. In both case you presented here, before writing out the Jacobian matrix, recall the formal definition of each term, and see how it applies here.
You'll see you'll end up with the same jacobian matrices.
((Basically what you do here, in your exemple, is permutting x_1 and x_2 in one side of the equation but not everywhere in the Jacobian definition. That's why you should understand formulas and not just copy and fill the blanks...))
That's because nothing can map reality, but reality itself. Perhaps one of these days a future super computer might spend a billions hours accurately rendering a single particle, as though it was real, but that will be about it.
...
>Explain to me why it should matter
It should matter because you have to be logically consistent. This user pretty much explained it.
Shit, I got it know. Thanks.
Wrong. user's right, though. The truth is it actually doesn't matter (what makes sense physically), the problem was that I was being a brainlet playing wrong with the definitions.
The how do you explain this [math] \mathbb{R} [/math]?
unrelated but i have never seen paper with those larger oval shaped holes underneath the circular ones. what country are you in?
did you pass dynamic systems? Your understanding of modeling is abysmal.
You're welcome !
Be sure to always be careful with that !
France ; it is to suit different way of classification we got here.