Talk:Outer product

message: Isn't this page redundant? It should be merged with exterior power. This page purports to define wedge product, however wedge product currently links to the exterior algebra page. -- Fropuff 19:34, 2004 May 20 (UTC)
:The exterior product or wedge product, in the context of exterior algebra, is defined very differently from the outer product presented here today (it might have been different in 2004, qhen you wrote your comment). An outer product returns a matrix. An exterior product creates a multivector. Paolo.dL 13:07, 19 May 2007 (UTC)
thread_title:  Outer product vs exterior product 

message: There is an error here:
 If W = V, then one can also pair w * (v), which is the inner product.
Inner product is a mapping from V \times V. Here we have mapping V^* \times V.
Natural correspondence between V and V^* exists only for Hilbert spaces
(See Riesz representation theorem for details).
Tenzink (talk) 10:30, 22 April 2008 (UTC)
replies: text: I don't think the correspondence is used here.  I think that w* denotes an element of the dual space W*.  (Not the dual of an element of W.)  That said, the section does take a rather idiosyncratic view towards the definition of an inner product.  silly rabbit (talk) 10:57, 22 April 2008 (UTC)
replies: text:  Agree. Tenzink (talk) 10:51, 23 April 2008 (UTC)
replies: text: As regards "Here we have mapping V^* \times V": May I request that in the future when referring to a mapping, could you please specify both a) the domain and b) the codomain. Thanks. 2601:200:C082:2EA0:782A:5C98:6D2F:A7C5 (talk) 01:47, 21 February 2023 (UTC)
thread_title:  Wrong note concerning inner product 

message: Should this page have a link to Dyadic product?  Or should the articles be merged?  They appear to be the same operation.206.207.225.87 (talk) 15:44, 9 April 2012 (UTC)
replies: text: Dyadic product, Tensor product and Outer product should all be considered as candidates for merging (IMO into Tensor product). — Quondum☏ 10:18, 19 August 2012 (UTC)
replies: text: Possibly. See here. Maschen (talk) 14:18, 21 August 2012 (UTC)
thread_title:  Dyadic Product 

message: Some people have proposed at WP Maths to transform this page into a disambiguation page. I also think it should be, but not immensely fussed if there are objections. Here is my draft, feel free to take or leave, provided a notification is made here and/or WP maths. Maschen (talk) 10:43, 24 August 2012 (UTC)
replies: text: Your draft is still slightly more like a stub than a disambiguation page, and will need minor changes to conform to the guidelines for a disambiguation page. The term is a little unusual in that it seems to be a minority use in every case, and this does not point to any article of the same name, so in a way it is more like a combined dab/redirect. Nevertheless, and I have no objection to it becoming one. — Quondum☏ 20:31, 24 August 2012 (UTC)
thread_title:  Transform to a disambiguation page?... 

message: I think that the explanation regarding the outer product rank is nearly totally incomprehensible. IMHO, a much simpler explanation is that matrix rows represent the same vector scaled differently. If you want to go into a few more details, you can explain that because of the above-mentioned property, for any two rows there obviously always exists a linear combination of these rows that is the zero vector. Likewise, you can nullify any combination of rows by picking two arbitrary rows and nullifying them while assigning zero coefficients for the remaining ones. Finally, you the rank will be one, because if u and v are non-zero, there will be at least one non-zero matrix element.  — Preceding unsigned comment added by Srchvrs (talk • contribs) 03:15, 13 July 2016 (UTC)
replies: text: The reasoning for the rank one property has been changed. The previous argument was missing why the scalar result means rank one. It also failed to mention use of associativity of multiplication being used. Maximal linear independence of columns usually establishes rank, and in the outer product matrix there is only one. — Rgdboer (talk) 22:57, 16 July 2018 (UTC)
thread_title:  Outer-product rank