Math can't model real systems

>>9087160
Or you're too much of a brainlet to use it correctly

>>9087160
>Interchanging rows changes eigenvalues
BRAINLET

File: Yes, it does..png (11KB, 779x608px) Image search: [Google]

11KB, 779x608px

>>9087310
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.

>>9087334
Pic related.

Changing rows of a matrix =/= changing order of the equation brainlet.

>>9087371
LOL

Now calculate them by hand both ways and read the documentation for the eig() function. You fucking brainlet.

>>9087334
it does though, consider the identity matrix vs [0 1; 1 0]

File: Lotka-Volterra model.jpg (2MB, 3264x1840px) Image search: [Google]

2MB, 3264x1840px

>>9089316
Then explain pic related (J is the jacobian matrix of the system and E.E. is the steady state solution).

>>9089325
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.

>>9089515
>inb4 it should be the square root of alpha times beta in the first case
I know. My point still stands though.

>>9087371
>>9089452
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.

>>9087160
>real systems
HAHAHAHAHAHAHAHAHAHAHA

>>9087371
>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.

>>9089535
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.

>>9089561
>Go ask an expert about it and you'll get a sensible answer.
I would if I could.

>>9089515
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...))

>>9087160
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.

File: DSC_1134.jpg (3MB, 3840x2160px) Image search: [Google]

3MB, 3840x2160px

>>9089515
>>9089619
>>9089624

>>9089619
>Explain to me why it should matter
It should matter because you have to be logically consistent. This anon >>9089648
pretty much explained it.

>>9089624
>>9089648
Shit, I got it know. Thanks.

>>9089675
Wrong. Anon'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]?

>>9089648
unrelated but i have never seen paper with those larger oval shaped holes underneath the circular ones. what country are you in?

>>9087160
did you pass dynamic systems? Your understanding of modeling is abysmal.

>>9089707
You're welcome !
Be sure to always be careful with that !

>>9089735
France ; it is to suit different way of classification we got here.