Talk:Cramer's rule

message: Any chance someone is willing to give a more precise statement of Cramer's rule?  As in the following:  Let R be a commutative ring, M a finitely generated R-module with generators m_i, and \phi:M\rightarrow M an endomorphism of R-modules.  \phi determines a matrix 
A=(a_{ij}) 
via \phi(m_i)=\sum a_{ij}m_j.  Then Adj(A)A=det(A)I, where Adj(A) is the cofactor matrix of A.
:That is not Cramer's rule, though it is related, but in a not so trivial way. There is no general rule for solving square linear systems over a commutative ring for the simple reason that they generally do not have unique solutions (try solving 3x=b in Z/6Z). Something can be said (if the determinant of the system happens to be an invertible element of the ring for instance) but I'm not sure this article is the right place. Marc van Leeuwen (talk) 14:55, 7 September 2009 (UTC)
replies: text: It might help if you say what you find hard to understand.  (For a WP math article, that version is pretty straight-forward!) -- Elphion (talk) 17:51, 8 January 2014 (UTC)
thread_title:  More precise statement 

message: am I right that there's nothing special about comparative statics, it's just an example of solving a system of linear equations, nothing particularly about cramer's rule.  This latest edit says it's of 'further significance', but it doesn't seem to be. --Tristanreid 
: I don't find that example much useful either. Oleg Alexandrov (talk) 23:52, 17 October 2005 (UTC)
replies: text: ok, I'm yanking it. Thanks for signing me, by the way.  I forgot last time. Tristanreid 02:44, 19 October 2005 (UTC)
thread_title:  Does the example of comparative statics in econ make any sense? 

message: Vilna Gaon seems to have come out of left field.  I note that the main article on him includes a similar statement without attribution.  Does anyone have a reference for this statement? S.N. Hillbrand 20:45, 22 December 2005 (UTC)
replies: text: Thanks for removing that. Looked like a strange edit. Oleg Alexandrov (talk) 01:25, 23 December 2005 (UTC)
thread_title:  Where did Gaon come from? 

message: About a year ago there was a beautiful proof of the Cramer's rule on this wikipedia page.
Can you, please, bring it back?
Thanks
Pavel.Pokorny@vscht.cz  —Preceding unsigned comment added by 147.33.113.54 (talk) 17:05, 6 December 2007 (UTC)
thread_title:  Where has the nice proof gone? 

message: The 4th image in the example section is incorrect. The determinant in the numerator is calculated in correctly. Sorry I cannot fix it right now,will someone else?--128.101.152.71 (talk) 21:12, 10 March 2008 (UTC)
replies: text: Done. Michael Slone (talk) 01:32, 11 March 2008 (UTC)
thread_title:  Incorrect Example 

message: ::"The numerator will always be zero, since here c=0."
I can't find any previous reference to c. Is this a remnant of an earlier edit? -- 72.224.136.152 (talk) 14:41, 23 September 2009 (UTC)
replies: text: OK, the problem came from an earlier edit. Variable c was changed to b but a later reference to it remained unchanged. -- TheMaestro (talk) 02:08, 24 September 2009 (UTC)

text: I agree, I think the connection to Cramer's rule is tangential at best, in more senses than one. -- TheMaestro (talk) 01:50, 25 September 2009 (UTC)
thread_title:  Re: Relevance to eigenvalues 

message: I would like to add a section to this article to provide a proof of cramers rule. The proof is on my user page.  Djwinters (talk) 00:56, 16 January 2010 (UTC)
replies: text: The proof is unclear in what it sets out to prove (the whole article could be clearer about the precise statement od Cramre's rule as well), and is phrased more like a recipe than like a proof. As far as I can tell it only aims at showing that the rule provides a solution in favorable cases (not that this is the only solution), and only works well if not only the denominator determinant is nonzero (which is part of the rule's hypotheses), but also all the individual xi in the solution. In other words I think the proof could be improved. It would also be good to provide a reference for this proof, or is it your own invention? Marc van Leeuwen (talk) 21:55, 16 January 2010 (UTC)

text: * I agree with the fact that other proves (maybe better ones) can be given. Now, I disagree with the fact that it doesn't work with systems with some zeroes in the solution. These are rational functions, there is a general principle (follows from analytic continuation and many other principles in complex analysis) that if these manipulations work for non-zero (as the proof shows) then it works in general. The uniqueness of the solution can be derived easily from the very statement of Cramer's formulas.  franklin  22:29, 16 January 2010 (UTC)
thread_title:  cramers rule proof 

message: This appears in the article:
: 
:: Cramer's rule can be used to prove that an integer programming problem whose constraint matrix is totally unimodular and whose right-hand side has integer basic solutions.
: 
Someone forgot to finish the sentence. Michael Hardy (talk) 03:44, 30 March 2010 (UTC)
thread_title:  Mangled sentence 

message: This section of the article seems to be out of place.  There is apparently no use made of Cramer's rule in finding the inverse matrix and no use made of inverse matrices elsewhere in the article.  Should we remove it? SpinningSpark 17:38, 17 July 2010 (UTC)
thread_title:  Finding inverse matrix 

message: There are two claims of the time complexity of the rule: is it O(n*n!) or is it O(n^3)? 161.31.73.176 (talk) 16:01, 29 January 2016 (UTC)
thread_title:  Time Complexity 

message: I want to learn how to calculate complementaru angles Gavazacarol (talk) 16:22, 4 May 2016 (UTC)
thread_title:  maths 

message: I could be very wrong about this, but isn't cramer's closely related to the history of the determinant? That should probably be mentioned or at least linked here, but preferably it could have its own section.
Gyinagal (talk) 01:03, 28 September 2020 (UTC)
thread_title:  Cramer's rule and the determinant