| 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 | |