[Merged by Bors] - feat(analysis/normed_space/inner_product): existence of orthonormal basis #5734
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Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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| @@ -595,12 +595,20 @@ lemma prod_ite_eq (f : α →₀ M) (a : α) (b : α → M → N) : | |||
| f.prod (λ x v, ite (a = x) (b x v) 1) = ite (a ∈ f.support) (b a (f a)) 1 := | |||
| by { dsimp [finsupp.prod], rw f.support.prod_ite_eq, } | |||
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| @[simp] lemma sum_ite_self_eq {N : Type*} [add_comm_monoid N] (f : α →₀ N) (a : α) : | |||
| f.sum (λ x v, ite (a = x) v 0) = f a := | |||
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ite (a = x) v 0 is basically finsupp.single x v a, for which there are plenty of lemmas about. Does the ite appear in your proof in a place where finsupp.single could be used instead?
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Although this lemma is probably good to have anyway
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I didn't succeed in massaging the use (it's in orthonormal.inner_right_finsupp) to this form.
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…asis (#5734) Define `orthonormal` sets (indexed) of vectors in an inner product space `E`. Show that a finite-dimensional inner product space has an orthonormal basis. Co-authored by: Busiso Chisala
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…asis (#5734) Define `orthonormal` sets (indexed) of vectors in an inner product space `E`. Show that a finite-dimensional inner product space has an orthonormal basis. Co-authored by: Busiso Chisala
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Define
orthonormalsets (indexed) of vectors in an inner product spaceE. Show that a finite-dimensional inner product space has an orthonormal basis.Co-authored by: Busiso Chisala