The Lie algebra rank condition for a planar bilinear control system holds exactly when some two matrices in the generated Lie algebra have an adjoint product with complex eigenvalues.
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Lie algebra rank condition for bilinear control systems on $\mathbb{R}^2$
The Lie algebra rank condition for a planar bilinear control system holds exactly when some two matrices in the generated Lie algebra have an adjoint product with complex eigenvalues.