= Eigendirection
{title2=$\operatorname{span}\{v\},\qquad Av=\lambda v,\ v\ne0$}
An <eigendirection> is the one-dimensional <vector subspace> spanned by an <eigenvector>. Multiplying the <eigenvector> by a nonzero <scalar> leaves this direction unchanged. In a planar linear <dynamical system>, a negative real <eigenvalue> gives a direction of exponential approach to the <equilibrium point>, while a positive one gives exponential departure. For a hyperbolic <saddle equilibrium>, the nonlinear <stable manifold> and <unstable manifold> are tangent to the corresponding <eigendirections>.
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