Talk:Homogeneous function

message: What the hell is x times gradient of f(x) supposed to mean, dot product?
:It means that for a vector function f(x) that is homogenous of degree k, the dot production of a vector x and the gradient of f(x) evaluated at x will equal k * f(x). CodeLabMaster 12:12, 05 August 2007 (UTC)
replies: text: Yes, as can be seen from the furmula under that one. I've added the dot and changed vector symbols to bold. mazi 18:04, 22 February 2006 (UTC)
thread_title: [Untitled Section]

message: The article, before I changed it a moment ago, implied that all homogeneous functions are differentiable. Here's a counterexample: f\colon \mathbb R^2 \to \mathbb R, k=1, with f(x,y)= x (if xy>0) or 0 (otherwise). --Steve 03:23, 6 August 2007 (UTC)
thread_title:  Not all homogeneous functions are differentiable 

message: According to planetmath , the theorem about derivatives is not correct unless we replace "homogeneous" by "positive homogeneous" throughout. Their counterexample is wrong (I just submitted a correction on the site), but could that claim be correct? Does anyone have a reference, or a proof, or a proper counterexample?
Update: The person maintaining that planetmath page responded to my correction by taking away the counterexample but keeping the claim. Again, a reference, proof, or proper counterexample is needed to resolve this. --Steve 15:51, 5 October 2007 (UTC)
thread_title:  Is the derivative theorem correct? 

message: Notation such as
:\frac{\partial f}{\partial x_1} (\alpha \mathbf{x}) 
can be confusing: Are we differentiating the expression with respect to the first component of \mathbf{x} or do we mean the partial derivative of f with respect to its first argument evaluated at the point \alpha \mathbf{x} ?
It's therefore better to write
:\frac{\partial f}{\partial x_1} (\alpha \mathbf{y}) :
now it's clear that x_1,\ldots, x_n are the arguments of f and we are differentiating with respect to the first argument of f evaluated at the point \alpha \mathbf{y} . 
I've cleaned up the notation in my proof of Euler's theorem accordingly. 91.21.25.30 (talk) 21:50, 11 February 2008 (UTC)
replies: text: I agree. Sorry about my incorrect edit to that effect earlier, thanks for reverting :-) --Steve (talk) 18:00, 11 February 2008 (UTC)
thread_title:  Notation 

message: Euler's theorem? why the name, is he the 1st guy prove this? if yes, why don't we use his work as a reference? Jackzhp (talk) 17:29, 4 December 2008 (UTC)
replies: text: Keep in mind the Euler lived in the 18th century and wrote mostly in Latin so not really a good reference for a modern audience. It might be worth adding the original work as a historical reference though.--RDBury (talk) 21:44, 18 April 2010 (UTC)
thread_title: the name

message: The Phi used in the equations, that is /varphi inside a <math> tag, was rendered differently in my browser (mobile Safari) than the &phi used in the descriptions below (see Phi#Computing) -- so I switched the descriptions to use the clumsier but definitely-consistent <math> tag construction. 184.17.182.96 (talk) 06:26, 21 December 2012 (UTC)
thread_title:  Note on change http://en.wikipedia.org/w/index.php?title=Homogeneous_function&diff=529079679&oldid=520543743 

message: People who look up homogeneous function may not necessarily understand what "ƒ : V → W is a function between two vector spaces over a field F"  means; Likewise people who know what a Banach space are not likely to wonder "what the heck is a homogeneous function" and look it up in Wikipedia. Do not scare people away from math please. And foremost, be mindful Wikipedia is basically an encyclopedia; it's meant for ordinary people to look up stuff :)  --Sahir 08:41, 8 December 2015 (UTC)
thread_title: Keep it simple please

message: In the second line, should it say f(ax,y) = a^kf(x,y) rather than f(ax,ty)=a^kf(x,y)? It looks like a typo but I don't know enough about the subject to edit. Mrdouglasweathers (talk) 12:35, 1 November 2016 (UTC)
replies: text: This makes sense. I fixed it. --Erel Segal (talk) 13:16, 1 November 2016 (UTC)
thread_title: Typo in the introduction?

message: How about an example of homogeneity of degree 0? Btyner (talk) 21:48, 1 September 2017 (UTC)
thread_title:  degree 0 example? 

message: The former is covered by the introduction, but that's it; later on, the square root is given as example, without discussing that it is not a function on a vector space. 
Absolute homogeneity is defined only later, but - being a defining property of norms - it could very well go into the introduction.
(And: Zero removed? What about "[...] e.g. making matrix rank homogeneous of degree zero, once one omits the exceptional s=0".)  — Preceding unsigned comment added by 193.90.163.192 (talk) 09:17, 6 December 2021 (UTC)
thread_title:  functions defined on positive cones or rays - and absolute homogeneity