An extrinsic symmetric space is a submanifold M ⊂ V = Rⁿ which is kept invariant by the reflection sₓ along every normal space Nₓ M. An extrinsic symmetric subspace is a connected component M′ of the intersection M ∩ V′ for some subspace V′⊂ V which is sₓ-invariant for any x ∈ M′. We give an algebraic charactrization of all such subspaces V′.
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