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feat(linear_algebra/matrix_group): introduce matrix_group and instances #17608

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@vasnesterov vasnesterov commented Nov 18, 2022

introduce matrix_group typeclass
add a coercion to GL and proof some lemmas about it add a function special which produce special subgroup of a matrix group provide GL, U, O, SL, SU, SO as instances of matrix_group

It's my very first PR, so I'm super open to any criticism and suggestions (about github usage, Zulip usage, code style, proofs (I think sometimes they are much longer than they could be, actually I only know the basic tactics so far), naming and so on).

…nstances

introduce matrix_group typeclass
add a coercion to GL and proof some lemmas about it
add a function special which produce special subgroup of a matrix group
provide GL, U, O, SL, SU, SO as instances of matrix_group
@vasnesterov vasnesterov added awaiting-review The author would like community review of the PR undergrad Relates to undergrad.yaml t-algebra Algebra (groups, rings, fields etc) labels Nov 18, 2022
replace ```has_coe``` with ```has_coe_t```
set low priority to ```coe_is_monoid_hom_trans```
swap "special" and "examples" sections
format curly braces
make all lines no longer than 100
@YaelDillies
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I'm sorry, coe_is_monoid_hom was wiped out of existence recently in order to facilitate the port. This compromises your matrix_group approach.

What item on https://leanprover-community.github.io/undergrad_todo are you claiming this solves, btw? I'm not sure matrix_group is any more interesting than (f : G →* GL n R) (hf : function.injective f).

@YaelDillies YaelDillies added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Feb 24, 2023
@semorrison semorrison added the too-late This PR was ready too late for inclusion in mathlib3 label Jul 16, 2023
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awaiting-author A reviewer has asked the author a question or requested changes t-algebra Algebra (groups, rings, fields etc) too-late This PR was ready too late for inclusion in mathlib3 undergrad Relates to undergrad.yaml
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