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chore: forward-port leanprover-community/mathlib#18558 #2719

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@eric-wieser eric-wieser added mathlib3-pair This PR is a forward-port of a mathlib3 PR or part of one, either under review or recently merged awaiting-CI labels Mar 8, 2023
@eric-wieser eric-wieser added the awaiting-author A reviewer has asked the author a question or requested changes label Mar 8, 2023
bors bot pushed a commit to leanprover-community/mathlib that referenced this pull request Mar 8, 2023
…18558)

This:
* Generalizes `is_self_adjoint.smul`, which makes it easier to show that `0.5 • x` is self-adjoint when `x` is, even if `0.5` is a complex number.
* Generalizes `is_self_adjoint.add` to match `matrix.is_hermitian.add` (for a later refactor), along with many other lemmas.
* Removes re-proofs of `star_nat_cast` and `star_int_cast`.

The first is motivated by showing that `exp K m` for some matrix `m` is positive definite if `is_self_adjoint m`.

Forward-ported at leanprover-community/mathlib4#2719.
@semorrison semorrison added merge-conflict The PR has a merge conflict with master, and needs manual merging. and removed awaiting-CI labels Mar 27, 2023
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Duplicate of #3159

@eric-wieser eric-wieser marked this as a duplicate of #3159 Mar 31, 2023
@int-y1 int-y1 deleted the forward-port-18558 branch April 16, 2023 18:26
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