Determinant and Adjugate Matrix#1165
Conversation
There was a problem hiding this comment.
This looks like accidentally committed files
There was a problem hiding this comment.
Yes. I have removed it.
|
Thanks for opening a PR on this! Determinants would certainly be very useful to have. |
| @@ -0,0 +1,194 @@ | |||
| {-# OPTIONS --cubical #-} | |||
|
|
|||
| module Minor where | |||
There was a problem hiding this comment.
Module names should always be fully qualified, i.e. Cubical.Algebra.Determinant.Minor in this case.
There was a problem hiding this comment.
Thank you! I have fixed it.
| CommRingR' : CommRingStr (R' .fst) | ||
| CommRingR' = commringstr 0r 1r _+_ _·_ -_ (CommRingStr.isCommRing (snd P')) | ||
|
|
||
| -- Definition of the minor factor |
There was a problem hiding this comment.
I noticed that there is some redundancy in the Determinat (is that a typo?) .Base file. MF i is just (- 1r) ^ i (_^_ is defined in Cubical.Algebra.CommRing.Properties, and many of the properties of minor factor you prove are already proved there). And +Compat can by proved more simply by cong₂ _+_.
There was a problem hiding this comment.
Thank you! That could very well be the case. There is certainly a lot to improve here. When I wrote that, I had just started with Agda.
…c000fafb882e5b6046408f6993e0" This reverts commit e7aee8949ba8708c0ffbdb8f8d21fbdb13af6153.
Some fixes for your PR on determinants
|
What is the state of this PR? Has all comments been addressed so that it's ready for another round of reviews/merging? |
|
I honestly don't remember - I think I had a discussion with @FranziskusWiesnet which might not have taken place here. At a quick glance I only see |
|
Thanks for checking in! Since this PR has been open for quite some time, I do not remember all details either. Could someone start another round of review? I would be happy to address any remaining issues. |
4 participants
In the four new files, the determinant of a matrix over a commutative ring is introduced through Laplace expansion, and it is proven that the adjugate matrix multiplied by the matrix itself equals the determinant times the identity matrix.
Additionally, it is shown that the determinant is independent of the row or column chosen for expansion, along with a few other minor properties of the determinant.
I am happy to consider any improvements.