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refactor(analysis/normed_space/operator_norm): extend from R to any field#821
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sgouezel wants to merge 5 commits intoleanprover-community:masterfrom
Closed
refactor(analysis/normed_space/operator_norm): extend from R to any field#821sgouezel wants to merge 5 commits intoleanprover-community:masterfrom
sgouezel wants to merge 5 commits intoleanprover-community:masterfrom
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jcommelin
reviewed
Mar 16, 2019
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Author
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Rebased. Should be ready for merging. |
Member
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It's nice to see some of these proofs simplify! Looks good to me. Let's get this merged. |
Member
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@sgouezel Travis is unhappy. I think you need to bump up the type class search depth in some places. |
Collaborator
Author
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Done. |
Collaborator
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Merged ae8a1fb, but with the wrong commit message. Sorry about that. |
Collaborator
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@avigad your merge is broken because of type classes. Are you working on that? Otherwise, I would delete that commit from master. |
Collaborator
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@cipher1024 I tested it on my machine. Maybe it is the instance depth issue. How can I see the error message from Travis? |
Collaborator
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I see the fix by @ChrisHughes24 now. Chris, thanks for fixing it. |
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In the current version, the operator norm of a bounded linear map is defined as its supremum on the unit ball. This does not work if there are points in the space that can not be rescaled to be on the unit sphere. Therefore the definition is currently restricted to vector spaces over R.
We redefine the operator norm as the sup of ||A x||/||x|| for all x, extend to any normed field, and simplify some proofs.