= Center subspace
{title2=$E^c$}
= Centre subspace
{synonym}
For a finite-dimensional linearization $\dot v=Av$, the <center subspace> is the real invariant subspace associated with all generalized <eigenvectors> whose <eigenvalues> have zero real part. It includes zero eigenvalues and purely imaginary conjugate pairs. Generalized eigenspaces are needed when $A$ is not diagonalizable.
For $A=\operatorname{diag}(-1,0,2)$, it is the second coordinate axis. For a planar rotation matrix generator, it is the whole plane. The linear system alone gives no exponential contraction or expansion on this subspace; nonlinear terms can still cause growth or decay. A local <center manifold> is tangent to it at the equilibrium.
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