Eigenvector Problem

[GWestphal]

..

 

[toslat]

http://mathworld.wolfram.com/FixedPoint.html
see the table at the bottom

In your case, it is an unstable improper node.

 

[soccerballtux]

can anyone give a real world example where one might apply this stuff?
I want to be thinking about this but I can't find any reasons I need to know it.

 

[toslat]

Its applicable to any autonomous linear dynamical system governed by the relationship dX=Ax, where A is the state matrix.
The practical/physical implications of the type of fixed node, will depend on the original system/phenomenon that was modeled.
So do you want examples of what can be modeled as an LDS, or physical interpretation of fixed node types for a specific system?

 

[DeathRayLoveMachine]

Originally posted by: soccerballtux
can anyone give a real world example where one might apply this stuff?
I want to be thinking about this but I can't find any reasons I need to know it.

They're good for describing systems where:
a) you have a system of many interacting parts, and the state of those parts changes over time;
b) the changes that are about to occur depend on the state the system is currently in; and
c) the relationship between the current state and the changes that are about to happen is linear, or else the relationship can at least be approximated by a linear equation.

(Don't worry about what exactly the third part is supposed to mean. The gist of it is that the system can't be chaotic.)

Basically, eigenvectors are good for predicting oscillating systems (like car engines), systems that have stable "feedback loops" (like nuclear reactions), planetary systems, and stuff like that. They're NOT quite as good for predicting things that exhibit a "butterfly effect," like the weather (although eigenvectors can still be useful there, too).