Pensieve header: Plotting Phase Portraits.

PP[A_] := Show[VectorPlot[A.(({{x}, {y}})), {x,-1,1}, {y,-1,1}, Frame -> None],
ParametricPlot[Evaluate[Table[MatrixExp[t A].(({{Cos[θ]}, {Sin[θ]}})), {θ, π/4, 2π, π/4}]],{t,-π,π}, ColorFunction -> (Red&)],
ImageSize->150]

PP/@ {(({{-2, 0}, {0, -1}})), (({{-1, 0}, {0, 0}})), (({{-1, 0}, {0, 1}})), (({{0, 0}, {0, 1}})), (({{1, 0}, {0, 2}}))}

PP/@ {(({{-1, 0}, {0, -1}})), (({{0, 0}, {0, 0}})), (({{1, 0}, {0, 1}}))}

PP/@ {(({{-1, -1}, {1, -1}})),(({{0, -1}, {1, 0}})),(({{1, -1}, {1, 1}})),(({{3, -1}, {1, 3}})),(({{1, -2}, {2, 1}}))}

PP/@ {(({{-1, 1}, {0, -1}})),(({{0, 1}, {0, 0}})),(({{1, 1}, {0, 1}}))}