Talk:Kronecker product

Request

Requesting addition/articles for Khatri-Rao and Tracy-Singh products. [1] Shyamal 04:39, 25 July 2006 (UTC)

 Done - actually a few months ago. -- StevenDH (talk) 20:23, 16 April 2008 (UTC)

add bases to comparison to abstract tensor product

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

 Done - actually a few months ago, as well. RobHar (talk) 16:18, 18 August 2009 (UTC)

Column-wise Khatri-Rao product

An anonymous user edited (concerning the final related matrix operation):

<!-- comment: the following definition is the same as the above except that it uses implicit partitions instead of explicit partitions... is there really need for this second example? -->

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)

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)

Question!!!

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)

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)

Link to the article in Russian is missing

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