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[Merged by Bors] - feat(analysis/normed_space/inner_product): isometry of ℂ with Euclidean space #6877

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is isometric to fin 2 → ℝ with the Euclidean inner product. The isometry given here is that defined by the ordered basis {1, i} for .


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https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/.60inner_product_space.20.E2.84.9D.20%28euclidean_space.20.F0.9D.95.9C.20n%29.60.3F/near/230766844

@hrmacbeth hrmacbeth added the awaiting-review The author would like community review of the PR label Mar 26, 2021
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urkud commented Mar 26, 2021

Are the formulas for to_map/inv_map a part of the public API? If yes, could you please provide lemmas?

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See what you think of the material I just added. The inv_fun apply lemma is easy to state, the to_fun one is a bit more awkward, let me know if you have a better formulation.

Co-authored-by: Yakov Pechersky <pechersky@users.noreply.github.com>
@hrmacbeth hrmacbeth changed the title feat(analysis/inner_product): isometry of ℂ with Euclidean space feat(analysis/normed_space/inner_product): isometry of ℂ with Euclidean space Mar 27, 2021
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bors r+
Thanks!

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Mar 30, 2021
bors bot pushed a commit that referenced this pull request Mar 30, 2021
…an space (#6877)

`ℂ` is isometric to `fin 2 → ℝ` with the Euclidean inner product.  The isometry given here is that defined by the ordered basis {1, i} for `ℂ`.
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bors bot commented Mar 30, 2021

Pull request successfully merged into master.

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@bors bors bot changed the title feat(analysis/normed_space/inner_product): isometry of ℂ with Euclidean space [Merged by Bors] - feat(analysis/normed_space/inner_product): isometry of ℂ with Euclidean space Mar 30, 2021
@bors bors bot closed this Mar 30, 2021
@bors bors bot deleted the complex-isometry-pi branch March 30, 2021 14:01
b-mehta pushed a commit that referenced this pull request Apr 2, 2021
…an space (#6877)

`ℂ` is isometric to `fin 2 → ℝ` with the Euclidean inner product.  The isometry given here is that defined by the ordered basis {1, i} for `ℂ`.
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4 participants