feat(Analysis/Normed/Operator): definition of singular values for linear maps

[nielsvoss]

This PR defines a generalization of singular values, the approximation numbers, for continuous linear maps between normed vector spaces. It proves basic lemmas about the approximation numbers and shows that for finite-dimensional vector spaces, the approximation numbers coincide with the standard definition of singular values.

See the discussion on Zulip: https://leanprover.zulipchat.com/#narrow/channel/217875-Is-there-code-for-X.3F/topic/Singular.20Value.20Decomposition/with/558914024

Co-authored-by: Arnav Mehta [email protected]
Co-authored-by: Rawad Kansoh [email protected]

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[nielsvoss]

WIP

[github-actions]

PR summary 46c21b0013

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

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You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).