線形[{{a11_,a12_},{a21_,a22_}}]:=Module[{A,f,g,b1,b2,F},
A={{a11,a12},{a21,a22}};
f[x_]:=A.x; b1=A.{1,0}; b2=A.{0,1};
y1=Table[Line[{k b1-b2,k b1+6b2}],{k,-1,6}];
y2=Table[Line[{-b1+k b2,k b2+6b1}],{k,-1,6}];
方眼={Thickness[0.002],{Dashing[{0.01}],y1,y2}};
F={{0,0},{1,0},{1,2},{3,2},{3,3},{1,3},{1,4},{4,4},{4,5},{0,5},{0,0}};
字={Red,Thickness[0.008], Line[F]};
像={Blue,Thickness[0.008],Line[Map[f,F]]};
g[x_]:={x,A.x};
矢={Thickness[0.00],Line[Map[g,F]]};
Show[Graphics[{方眼,像,字, 矢}],Axes->True,
PlotLabel->{{a11,a12},{a21,a22}},AspectRatio-> Automatic]]

線形[(({{3, -1}, {1, 2}}))]

{

StreamPlot[(({{3, -1}, {1, 2}})).{x,y},{x,-5,5},{y,-5,5}]

mult[v_]:={v,(({{3, 1}, {1, 2}})).v}

Map[mult,{{1,0},{1,2},{3,2},{3,3},{4,5},{5,5}}]