(* riesime x'=Ax 
obe vlastne cisla su realne zaporne *)

a11=-1;a12=0;a21=0;a22=-0.25;

A={{a11,a12},{a21,a22}};
MatrixForm[A]

Eigenvalues[A]
Eigenvectors[A]

riesenie=DSolve[{x'[t]==a11*x[t]+a12*y[t],y'[t]==a21*x[t]+a22*y[t],y[0]==y0,x[0]==x0},{x,y},t]

trajektoria[px_,py_,T]:=ParametricPlot[Evaluate[({x[t],y[t]}/.riesenie[[1]])/.{x0->px,y0->py}],{t,0,T},AspectRatio->Automatic,PlotRange->{{-2,2},{-2,2}},Ticks->{{-2,-1,0,1,2},{-2,-1,0,1,2}}]

T=7;
g[1]=trajektoria[0,2,T];
g[2]=trajektoria[2,2,T];
g[3]=trajektoria[-2,2,T];
g[4]=trajektoria[-2,1,T];
g[5]=trajektoria[2,1,T];

Show[Table[g[i],{i,1,5}]]

Manipulate[g=trajektoria[-2,2,it];Show[g],{it,0.1,7,0.1}]

a11=0;a12=1;a21=-1;a22=-0.25;
A={{a11,a12},{a21,a22}};
MatrixForm[A]

Eigenvalues[A]
Eigenvectors[A]

riesenie=DSolve[{x'[t]==a11*x[t]+a12*y[t],y'[t]==a21*x[t]+a22*y[t],y[0]==y0,x[0]==x0},{x,y},t]

T=7;
t[1]=trajektoria[0,2,T];
t[2]=trajektoria[2,2,T];
t[3]=trajektoria[-2,2,T];
t[4]=trajektoria[-2,1,T];

Show[Table[t[i],{i,1,4}]]