Normed vector types, infinite norm, norm equivalence thm, continuity … #1718
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…of linear functions in finite dimension
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@mkerjean FYI |
| Let V' := @fullv _ V. | ||
| Hypothesis (Bbasis : basis_of V' B). | ||
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| Definition oo_norm x := \big[Order.max/0]_(i < \dim V') `|coord B i x|. |
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Is it really a good name? Because it is a bit like using a notation inside an identifier, also we have been using oo to mean "open-open" in MathComp (when talking about intervals). What about infty_norm? (like in LaTeX). Possibly coupling it with a notation using +oo in some way.
CohenCyril
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Oct 16, 2025
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| Lemma equivalence_norms (N : V -> R) : | ||
| N 0 = 0 -> (forall x, 0 <= N x) -> (forall x, N x = 0 -> x = 0) -> | ||
| (forall x y, N (x + y) <= N x + N y) -> | ||
| (forall r x, N (r *: x) = `|r| * N x) -> | ||
| exists M, 0 < M /\ forall x : Voo, `|x| <= M * N x /\ N x <= M * `|x|. |
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I think this deserve an abstraction of norm and an abstraction of norm comparison :)
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Continuity of linear functions in finite dimension
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