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cead56f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | import OAI.Geometry.ProjectionBody.Definitions
namespace OAI
noncomputable section
namespace ProjectionCounterexample
@[simp] theorem project_self {d : ℕ} (u : E d) : project u u = 0 :=
Submodule.starProjection_orthogonalComplement_singleton_eq_zero u
theorem project_ker {d : ℕ} (u : E d) :
(project u).toLinearMap.ker = Submodule.span ℝ {u} := by
change (ℝ ∙ u)ᗮ.starProjection.ker = ℝ ∙ u
rw [Submodule.ker_starProjection, Submodule.orthogonal_orthogonal]
end ProjectionCounterexample
end
end OAI
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