November 10, 2015

This function takes a 2x2 matrix A as its input and plots the eigenvectors of A and the flow lines formed by iterating (A^k)x. 
The default plot region is [-5,5] x [-5,5], but you can adjust this by changing the parameter k within the function. 

Note that the flow lines are only valid for positive eigenvalues.

DynamPlot[A_]:=Module[{p1,p2,p3,x,y, k},
k = 5; 
p1=StreamPlot[ Transpose[A.Transpose[{{x,y}}]][[1]]-{x,y},{x,-5,5},{y,-k,k},StreamScale->Large];
p2=ParametricPlot[t*Normalize[ Eigenvectors[A][[1]]],{t,-k,k},PlotStyle->{Red,Thickness[0.01]}];
p3=ParametricPlot[t*Normalize[ Eigenvectors[A][[2]]],{t,-k,k},PlotStyle->{Green,Thickness[0.01]}];
Show[p1,p2,p3]]

DynamPlot[{{2,0},{0,3}}]

A=1/7{{18,2},{6,17}}
DynamPlot[A]

Eigensystem[A]//MatrixForm