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[Merged by Bors] - feat(linear_algebra/char_poly/coeff,*): prerequisites for friendship theorem #3953

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adds several assorted lemmas about matrices and zmod p
proves that if M is a square matrix with entries in zmod p, then tr M^p = tr M, needed for friendship theorem


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@awainverse awainverse added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Aug 28, 2020
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This should fix the linter errors.

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awainverse and others added 2 commits August 28, 2020 21:52
Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
Co-authored-by: Bryan Gin-ge Chen <bryangingechen@gmail.com>
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Thanks! I think two lemmas could be simp. After that, go ahead an tell bors to merge it 🐙

bors d+


variables {p : ℕ} [fact p.prime]

lemma finite_field.char_poly_pow_card {K : Type*} [field K] [fintype K] (M : matrix n n K) :
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Thanks for this generalization!

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bors bot commented Aug 29, 2020

✌️ awainverse can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

awainverse and others added 2 commits August 29, 2020 09:19
Co-authored-by: Johan Commelin <johan@commelin.net>
Co-authored-by: Johan Commelin <johan@commelin.net>
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bors r+

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bors bot commented Aug 29, 2020

Canceled.

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bors r+

bors bot pushed a commit that referenced this pull request Aug 29, 2020
…theorem (#3953)

adds several assorted lemmas about matrices and `zmod p`
proves that if `M` is a square matrix with entries in `zmod p`, then `tr M^p = tr M`, needed for friendship theorem




Co-authored-by: Aaron Anderson <awainverse@gmail.com>
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bors bot commented Aug 29, 2020

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(linear_algebra/char_poly/coeff,*): prerequisites for friendship theorem [Merged by Bors] - feat(linear_algebra/char_poly/coeff,*): prerequisites for friendship theorem Aug 29, 2020
@bors bors bot closed this Aug 29, 2020
@bors bors bot deleted the friendship_prereq branch August 29, 2020 18:46
robertylewis pushed a commit that referenced this pull request Aug 31, 2020
…theorem (#3953)

adds several assorted lemmas about matrices and `zmod p`
proves that if `M` is a square matrix with entries in `zmod p`, then `tr M^p = tr M`, needed for friendship theorem




Co-authored-by: Aaron Anderson <awainverse@gmail.com>
PatrickMassot pushed a commit that referenced this pull request Sep 8, 2020
…theorem (#3953)

adds several assorted lemmas about matrices and `zmod p`
proves that if `M` is a square matrix with entries in `zmod p`, then `tr M^p = tr M`, needed for friendship theorem




Co-authored-by: Aaron Anderson <awainverse@gmail.com>
@YaelDillies YaelDillies removed the awaiting-review The author would like community review of the PR label Nov 15, 2021
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9 participants