Talk:Kronecker product

message: Is it possible to insert a reference in which one can find proofs for the listed properties of the Kronecker product? E.g. Abstract properties / 1. Spectrum needs in my opinion a citation.  — Preceding unsigned comment added by 161.116.80.135 (talk) 15:55, 10 September 2012 (UTC)
replies: text: I'm just going to add it in anyway and let the regulars of the article verify the references. jd22292 (Jalen D. Folf) (talk) 16:58, 14 July 2017 (UTC)
thread_title:  References 

message: Requesting addition/articles for Khatri-Rao and Tracy-Singh products.  Shyamal 04:39, 25 July 2006 (UTC)
replies: text: - actually a few months ago. -- StevenDH (talk) 20:23, 16 April 2008 (UTC)
thread_title:  Request 

message: The paragraph should note that a choice of bases is involved: If A and B represent homomorphisms given certain bases of the involved vector spaces, the Kronecker product of A and B represents the tensor product of these homomorphisms with respect to certain bases of the tensor products of the domain and codomain vector spaces of the form a_1 x b_1, a_1 x b_2, ..., a_1 x b_n, a_2 x b_1, ... 84.190.181.201
: - actually a few months ago, as well. RobHar (talk) 16:18, 18 August 2009 (UTC)
thread_title:  add bases to comparison to abstract tensor product 

message: An anonymous user edited (concerning the final related matrix operation):
:
The reason I got me a Wikipedia-account in the first place was that I needed the definition of the colunm-wise KR product for my master's thesis, and I was tired of always looking in the paper by Liu.  Later I examined this paper in which I saw (on p.3 in the pdf) what I had by then found out namely that the Khatri-Rao product is implied to operate on matrices with as partitions their columns.  I wasn't  sure whether this would be a mistake or a different (and confusing) convention or something, therefore, and also for my own reference, I added it to the article as a seperate case.  But maybe it needs some clarification. -- StevenDH (talk) 20:23, 16 April 2008 (UTC)
replies: text: I was the anonymous user who added that. That's interesting to hear why you initially added it. As you can see, I changed the wording in the article to say that both may be called the KR product. I've used the KR product in a couple papers recently in which I just define it as implicitly partitioning columns to avoid any confusion. As it stands, I left the example you added because it probably is better to include both examples (it appears both definitions are used).24.91.117.221 (talk) 17:03, 26 May 2008 (UTC)
thread_title:  Column-wise Khatri-Rao product 

message: If A is n-by-n, B is m-by-m and   \mathbf{I}_k denotes the k-by-k identity matrix then we can define the Kronecker sum, \oplus, by
: \mathbf{A} \oplus \mathbf{B} = \mathbf{A} \otimes \mathbf{I}_m + \mathbf{I}_n \otimes \mathbf{B}.  
(Note that this is different from the direct sum of two matrices.)
But the denotion of Kronecker sum and Direct sum is equel!!! So is it mistake? Gvozdet (talk) 13:29, 18 August 2009 (UTC)
replies: text: Do you mean that they are both denoted by ⊕? That's not really problem. There aren't enough symbols in math so it's common to reuse symbols. I am surprised this is called the Kronecker sum in the first place though. RobHar (talk) 15:37, 18 August 2009 (UTC)
thread_title: Question!!!

message: http://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80%D0%BD%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D0%B8%D0%B7%D0%B2%D0%B5%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5  —Preceding unsigned comment added by 217.29.95.125 (talk) 14:23, 23 July 2010 (UTC)
thread_title:  Link to the article in Russian is missing 

message: Miller (1981) derives a formula for the inverse of sums of Kronecker products (p. 72) in the special case where the "last" matrix is of rank 1. Specifically, 
Let W = A x G + B x E, where rank(E) = 1. Then W^{-1} = A^{-1} x G^{-1} - T x G^{-1} E G^{-1} where T = ( A + g B )^{-1} B A^{-1} and g = trace(E G^{-1}). Miller also works out examples where G is the identity matrix and B is also of rank 1. Are these too detailed to include in the  page? If they are appropriate, I can add them. --Nathanvan (talk) 22:31, 1 January 2013 (UTC)
thread_title:  Formulas for the inverse of a sum of Kronecker products 

message: The section on Properties says:
"The operation of transposition is distributive over the Kronecker product:
:(\mathbf{A}\otimes \mathbf{B})^T = \mathbf{A}^T \otimes \mathbf{B}^T."
This can be made more generic by also including the complex case and considering the conjugate transpose instead:
:(\mathbf{A}\otimes \mathbf{B})^* = \mathbf{A}^* \otimes \mathbf{B}^*.
I think this is worth noting. I believe it is more trivial to see from this that distributiviness also holds for the real case with the transpose, than the other way around.
anoko_moonlight (talk) 11:15, 12 August 2013 (UTC)
thread_title:  Property on transpose can be conjugate transpose 

message: How does one pronounce A ⊗ B ? If there’s a standard way, I think it should be mentioned the first time the notation appears in the article. Loraof (talk) 17:28, 5 July 2018 (UTC)
thread_title:  Pronunciation 

message: Property 2 of the Kronecker product uses the MATLAB notation without explaining it (I suspect it is just a copy/paste of the paper quoted [3]), which is unclear. Moreover, there is more to it, and there is even an article about this fact : https://en.wikipedia.org/wiki/Commutation_matrix. Perhaps the page should be edited to fill in the gaps and clarify this "Shuffle matrix" thing ? AnthonyStC (talk) 21:33, 6 August 2020 (UTC)
thread_title:  Perfect shuffle matrices and Commutation matrices