Talk:Matrix calculus

message: Could someone knowlagable please add a section on this? The current article only has matrix differentiation, not integation.--Maschen (talk) 10:51, 3 December 2011 (UTC)
thread_title: Matrix integration?

message: I believe information from:
:http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/IFEM.AppD.d/IFEM.AppD.pdf
:https://nrich.maths.org/discus/messages/7601/150862.html?1302548396
:http://planetmath.org/encyclopedia/DerivativeOfInverseMatrix.html
Should be integrated into this article or the creation of a new article talking specifically about many of these properties.  — Preceding unsigned comment added by 150.135.222.177 (talk) 19:50, 17 February 2012 (UTC)
replies: text: See #Definition of matrix derivative above.  I can't think of a way to integrate it.  — Arthur Rubin  (talk) 06:44, 18 February 2012 (UTC)
thread_title:  Request for derivatives of inverse matrix identities 

message: I think this page appears as disaster for new comers. I've read it for several times and referred to several sources. According to my understanding, the notation used in the first few sections, like "chain rule", is the transpose of that in the last few sections, like "example. 
Can anyone help to make this clear? Or, simply placing a warning there will be much better than the current situation. 
Hupili (talk) 09:16, 18 March 2012 (UTC)
thread_title:  Unifying the Notation 

message: I rewrote this article almost entirely.  Now, rather than try (and fail) to stick to one notation when there's no consistency among the sources, I present all identities according to different possible notations.  Since there isn't even any self-consistency in notation in many sources, I separate all the identities according to type of numerator and denominator so that e.g. if a given source uses one type of layout for one numerator/denominator type and another layout for a different type, you can make sense by mixing and matching the appropriate identities.
I've elided entirely any discussion of derivatives that produce results beyond two dimensions (e.g. vector-by-matrix or matrix-by-matrix).  I'm aware that some authors have indeed defined such derivatives, but I don't have much experience with such larger-dimensional aggregates and I imagine the notation is even less consistent here than elsewhere -- at least vectors and matrices themselves are pretty well-defined.
Benwing (talk) 01:22, 6 April 2012 (UTC)
replies: text: You have. Thank you. =) F = q(E+v×B) ⇄ ∑ici 17:49, 6 May 2012 (UTC)
thread_title:  fixed notation, hopefully 

message: I have reorganized the article to make in an attempt to make it more accessible to non-experts. In this spirit I have put definitions toward the front and identities toward the end of the article, as well as choosing one notation (numerator layout) for the first few sections, leaving technical discussion about other notations further along in the article. 
Please give me any feedback on this. To make a major change like this one does have to make a number of small decisions, and I apologize if others feel that I have taken away clarity from one of the original sections by making it part of this new organization. Some immediate example are the sections 'usages' and 'relation to other derivatives', which have been moved to the new first section called 'Scope' because I feel they are important both to the expert and the novice in the subject. Of course, when I say novice I do not mean someone who has not math background, but someone with some knowledge of calculus and linear algebra who has never heard of a derivative involving a matrix.
Finally, the newly added discussion on differential form is very good, but is still mainly only in the identities section. Perhaps we could move some of the initial discussion of differential form into the notation section, or in each of the definition sections.  — Preceding unsigned comment added by Brent Perreault (talk • contribs) 15:18, 18 May 2012 (UTC)
replies: text: Those edits were probably fine, thanks for the good faith and helpful edits. =) Moving things around for better continuity isn't a problem, by all means do so, if you think it will be better. F = q(E+v×B) ⇄ ∑ici 17:08, 18 May 2012 (UTC)
thread_title:  Re-Organized the article 

message: I was surprised to see that this article uses "unfortunately" four times. This seems odd - it's surely not up to an encyclopaedia to editorialize about what is or is not unfortunate, especially in a topic like this. I'm hoping that someone with knowledge of the topic can, without losing meaning, replace these with something more appropriate. Thanks and best wishes 82.45.217.156 (talk) 17:04, 7 June 2012 (UTC)
thread_title:  Unfortunately 

message: I would really appreciate if someone explained to me why in the numerator layout
\frac{\partial \mathbf{x}^{\rm T}\mathbf{A}}{\partial \mathbf{x}} = \mathbf{A}^{\rm T}.
The dimension of \mathbf{x}^{\rm T}\mathbf{A} is 1xn, the dimension of \mathbf{x} is nx1, thus according to the numerator layout the dimension of the result should be 1xn. 
All in all, this derivative looks like a derivative of a row vector by a column vector which is hard to interpret. 
According to this identity, in a singular case (A=I), we would have \frac{\partial \mathbf{x}^{\rm T}}{\partial \mathbf{x}} = \mathbf{I} = \frac{\partial \mathbf{x}}{\partial \mathbf{x}}. Was it the intention?
Thanks,
Sd1074 (talk) 20:03, 1 July 2012 (UTC)
thread_title:  Not a numerator layout in the numerator column?? 

message: I was wondering which CAS supports performing matrix calculus operations?
I know Sage/Maxima can do tensor calculus, but the extensions do not work well with inverses or determinants. The list of CAS tools do not have a column comparing this functionality either. I am hoping someone can provide a list of tools which can automate this process/check my work.  — Preceding unsigned comment added by 68.228.41.185 (talk) 04:11, 14 February 2013 (UTC)
thread_title:  Computer Algebra Software (CAS)? 

message: When one writes {\rm tr} in TeX one does not get proper spacing before and after "tr".  Thus:
:  a {\rm tr} B \,  is coded as    a {\rm tr} B, and
:  a \operatorname{tr} B \,  is coded as   a \operatorname{tr} B, and
:  a \operatorname{tr} (B) \,  is coded as   a \operatorname{tr} (B).
Writing \operatorname{tr} results in a certain amount of space before and after tr, and there is less space when (round brackets) follow tr than when they don't.  The form {\rm tr}, on the other hand, involves no spacing conventions.  The form \operatorname{tr} is standard usage and I edited accordingly. Michael Hardy (talk) 21:25, 7 February 2016 (UTC)
thread_title:  {\rm tr} is not the same as \operatorname{tr}. 

message: Not the same topic? Ardomlank (talk) 23:10, 31 March 2016 (UTC)
replies: text: No more than Calculus and Mathematical analysis are. Highly related but not the same. -Apocheir (talk) 18:42, 22 February 2020 (UTC)
thread_title:  [[Matrix analysis]] 

message: At each of the following spots, there's a scalar-by-matrix example labeled "numerator layout," but the examples aren't using the same layout, so one of them must be wrong (the first I think?):
https://en.wikipedia.org/wiki/Matrix_calculus#Scalar-by-matrix
https://en.wikipedia.org/wiki/Matrix_calculus#Numerator-layout_notation  — Preceding unsigned comment added by 98.163.18.220 (talk) 13:42, 21 March 2020 (UTC)
thread_title:  Example says "numerator layout" but is actually "denominator layout"? 

message: At the start of this section on the "differential-form first" technique, the reader is warned: "It is often easier to work in differential form and then convert back to normal derivatives. This only works well using the numerator layout."
However, a helpful example a bit further up the page uses this "differential-form first" technique to get an answer for the denominator layout (according to the table just below it, anyway). Is there something wrong with the example? Or is the "differential-form first" technique actually fine for the denominator layout, too? Or should the aforementioned warning really say that the technique "only works well using the denominator layout"?
Perhaps someone with expertise in this area (not I, alas) could reconcile this contradiction.  — Preceding unsigned comment added by 98.163.18.220 (talk) 14:26, 21 March 2020 (UTC)
thread_title:  Section on "differential-form first" technique could use some clarification re numerator vs denominator layout 

message: In Matrix-by-scalar identities, there is a row:
:
 Identities: matrix-by-scalar \frac{\partial \mathbf{Y}}{\partial x}
Condition         	Expression                                                 	Numerator layout, i.e. by Y
U = U(x), V = V(x)	\frac{\partial (\mathbf{U} \circ \mathbf{V})}{\partial x} =	\mathbf{U} \circ \frac{\partial \mathbf{V}}{\partial x} + \frac{\partial \mathbf{U}}{\partial x} \circ \mathbf{V}
If U = U(x) is a function of x, what is the meaning of  \mathbf{U} \circ \mathbf{V}? 78.91.103.181 (talk) 10:57, 6 August 2021 (UTC)
thread_title:  What is the meaning of <math>\mathbf{U} \circ \mathbf{V}</math>