Talk:Second partial derivative test

message: It says in the article that in higher dimensions you need to look at the eigenvalues. However, as is clearly explained in the article on positive definite matrix, it is possible to simply evaluate the 'leading principal minors' of the matrix (ie, the determinants of the upper-left square submatrices of sizes 1, 2, 3,..., n). If they are all positive, the Hessian is positive definite and we have a minimum. If the first one is negative and they alternate sign, then the Hessian is negative definite and we have a maximum. This method is much simpler than calculating the eigenvalues, as it does not require us to actually solve any non-linear polynomial equation. 140.180.55.46 (talk) 04:46, 16 November 2011 (UTC)
replies: text: It's also POV; for many applications -- say, writing code, a numerical computation of the Hessian is more feasible than writing an algorithm to qualitatively analyze the level curves.  Saying that one method is "overdoing it" compared to another is a bias.  --Heath 198.82.167.78 (talk) 22:54, 17 September 2008 (UTC)
replies: text: I think "overdoing it" was meant more for people analyzing simple surfaces (planes, paraboloids, the like), in which case it would be ridiculous to bother using the second derivative test. Nonetheless, it's not all that helpful and I don't find it contributes to the article; it's strictly about the SDT and not surface analysis. Section removed. StoicalSoul (talk) 01:47, 5 October 2008 (UTC)
thread_title: Method to shift the Hessian in higher dimensions

message: I’d wonder what geometric interpretation the determinant has in this case. Does it even have one? Suppose we have a function in which M > 0 and fxx < 0 for all (x,y), then there can only exist one maximum? - Or can one conclude this one the basis of M > 0 alone?
Perhaps this should be further explained in the article!?.
Sorry for the bad English! --83.72.7.63 (talk) 14:19, 14 January 2008 (UTC)
thread_title: The geometric Interpretation of the determinant

message: In the geometric intuition example, what does it mean when it says "between the x and y axis"?  How can you be between axes?71.33.4.235 (talk) 01:20, 28 April 2013 (UTC)
thread_title: I don't get...

message: The example of finding the critical points of  z = (x+y)(xy + xy^2)  has an error. 
: \frac{\partial z}{\partial y} = x \left( 3(-2x)^2 +2(-2x)(x+1) + x \right) = x^2(8x-3) \ne 4x^2(2x-1) 
Thus the point  (\frac{1}{2}, -1)  is not a critical point, while  (\frac{3}{8}, -\frac{3}{4})  is.
Including a plot of  z = (x+y)(xy + xy^2)  would really aid understanding of the example.
Adamace123 (talk) 14:14, 14 October 2008 (UTC)
replies: text: fixed Semifinalist (talk) 15:24, 25 August 2010 (UTC)
thread_title:  Error in example 

message: Hessian_matrix#Second_derivative_test discusses the same thing as this article and even does it better. This page and that section should be somehow merged, I think. - X7q (talk) 08:21, 15 May 2009 (UTC)
thread_title:  Duplicate content 

message: Please explain what M stands for in the geometric interpretation explantion of a 2-D hessian.  — Preceding unsigned comment added by Shreya.bits (talk • contribs) 04:36, 21 May 2013 (UTC)
replies: text: If I'm not mistaken M=D, so this is probably just a typo.--Kmhkmh (talk) 05:24, 21 May 2013 (UTC)
replies: text: Yes, it had previously been M for half the article and D for half, and when I standardized it seems I missed a couple of Ms.  JBL (talk) 13:33, 21 May 2013 (UTC)
thread_title:  Meaning of M in explanation of geometric interpretation 

message: In the section "Geometric interpretation in the two-variable case" a figure is desperately needed for the case where D<0 and both fxx and fyy have the same sign. This is the most interesting case and the most difficult to understand. A figure would really help here. -MATThematical (talk) 09:36, 18 October 2015 (UTC)
replies: text: Well, I have resolved this, but perhaps in a way you will not appreciate: I removed the section.  Someone with access to a couple decent multivariable calc books might be able to find a version of this with some sourcing, but what was written there struck me as mostly handwaving. --JBL (talk) 22:57, 18 October 2015 (UTC)
thread_title:  Figure Needed