ベクトル[{x1_,y1_},{x2_,y2_}]:=
Module[{線,a,b,c1,c2,c11,c12,d1,d2,d11,d12,e1,e2,矢},
a=x2-x1;b=y2-y1;
線={Thickness[0.002],Line[{{x1,y1},{x2,y2}}]};
c1=-a Cos[12 Degree]+b Sin[12Degree];
c2=-a Sin[12 Degree]-b Cos[12 Degree];
c11=x2+c1 0.5/(Sqrt[c1^2+c2^2]+0.0001);
c12=y2+c2 0.5/(Sqrt[c1^2+c2^2]+0.0001);
d1=-a Cos[-12 Degree]+b Sin[-12 Degree];
d2=-a Sin[-12 Degree]-b Cos[-12 Degree];
d11 = x2+d1 0.5/(Sqrt[d1^2+d2^2]+0.0001);
d12 = y2+d2 0.5/(Sqrt[d1^2+d2^2]+0.0001);
e1=x2-0.3 a/(Sqrt[a^2+b^2]+0.0001);
e2=y2-0.3b/(Sqrt[a^2+b^2]+0.0001);
矢=Polygon[{{x2,y2},{c11,c12},{e1,e2},{d11,d12},{x2,y2}}];
Graphics[{Blue, 線,矢}]];

ベクトル場[{{a11_,a12_},{a21_,a22_}}]:=
Module[{A},
A={{a11,a12},{a21,a22}};
Show[Table[ベクトル[{x1,y1},A.{x1,y1}],{x1,-5,5},{y1,-5,5}],
Axes->True,AspectRatio->Automatic,PlotRange->{{-8,8},{-8,8}}]];

A1={{1.1,0.2},{0.3,1}}

Show[ベクトル場[A1],
Graphics[{Red,Line[{7*{#1,-#1},7*{#2,-#2}}]}]
&[Eigenvectors[A1][[1]],Eigenvectors[A1][[2]]]]

A2={{1.3,0.1},{0.2,1.4}}

Show[ベクトル場[A2],Graphics[{Red,Line[{8*{#1,-#1},8*{#2,-#2}}]}
&[Eigenvectors[A2][[1]],Eigenvectors[A2][[2]]]]]

A3=(({{0.6, 0.2}, {0.4, 0.8}}))

Show[ベクトル場[A3],Graphics[{Red,Line[{6*{#1,-#1},7*{#2,-#2}}]}
&[Eigenvectors[A3][[1]],Eigenvectors[A3][[2]]]]]

A4={{1.2,-0.4},{0.5,1.1}}

ベクトル場[A4]

Eigenvalues[A4]

ベクトル場[(({{Cos[Pi/12], -Sin[Pi/12]}, {Sin[Pi/12], Cos[Pi/12]}}))]