Talk:Dyadic product

Question on dyadic product

Is the tensor product of a row vector $\mathbf {v}$ with a column vector $\mathbf {u}$ still called a dyadic product? For example:

$\mathbf {v} \otimes \mathbf {u} ={\begin{bmatrix}v_{1}&v_{2}&v_{3}\end{bmatrix}}\otimes {\begin{bmatrix}u_{1}\\u_{2}\\u_{3}\end{bmatrix}}={\begin{bmatrix}v_{1}u_{1}&v_{2}u_{1}&v_{3}u_{1}\\v_{1}u_{2}&v_{2}u_{2}&v_{3}u_{2}\\v_{1}u_{3}&v_{2}u_{3}&v_{3}u_{3}\end{bmatrix}}$

The indices in the definitions would have to be swapped in that case. --RainerBlome 21:28, 27 August 2005 (UTC)

Technically, tensor products of vectors (and vectors themselves) are defined without a particular matrix structure in mind (i.e., "row" versus "column" is unimportant), so the question is one of representation only. The ordering of (column) x (row) is chosen to match the intuition of matrix multiplication, creating a square matrix that represents the dyadic product of the two original vectors. The only reason for using "column vector" and "row vector" is to make their matrix representations intuitive, so if we're going to change or generalize anything, we should emphasize that "row" and "column" are only important in representing dyadic products, not in defining them. Shiznick 06:02, 8 May 2007 (UTC)

Proposed merge into Outer product

Why/how is this any different than the Outer Product? Should it be merged? —Preceding unsigned comment added by 132.170.160.64 (talk) 22:56, 31 March 2008 (UTC)

An outer product of two vectors produces another vector, while the dyadic product produces a second-order tensor, a matrix. So, no merger in my opinion. Crowsnest (talk) 23:50, 31 March 2008 (UTC)

Speaking absurd must be punished. --Javalenok (talk) 08:58, 10 September 2010 (UTC)

An outer product in fact yields a second-order tensor/matrix as well...In all honesty, I see no reason for this separate article. Dankatz316 (talk) 22:30, 15 May 2011 (UTC)

I oppose such a merge. Looking at Dyadics, it would seem that there is a similarity between a dyadic product and the tensor product of two vectors. To call the dyadic product a second-order tensor may not be such a good idea though: dyadics seems to be part of polyadics, and algebraic system similar to but not quite the full tensor algebra. The notation is a little different and to merge any mention of dyadics or polyadics into an article on tensors would only serve to make that article considerably more confusing. My suggestion is to keep the tensor and polyadics articles completely separate aside from a possible mention of their similarity. — Quondum^☏✎ 17:17, 15 January 2012 (UTC)

Merger of Dyadics into Dyadic product

I oppose to a merger of "dyadics" into this article, because

1. "dyadic product" is only a sub-operation of "dyadics", so if there has to be a merger, it has to be the other way around, and
2. "dyadic product" is the most used operation of the "dyadics", and deserves an article on its own.

Further, the "dyadics" article needs some wikification. Crowsnest (talk) 17:59, 18 July 2008 (UTC)

Undefined multiplication in 4th and 5th identities

Given that all u, v and w are vectors, I don't understand the unsigned multiplication used in the 4th and 5th identities of the paragraph "Identities". I usually use unsigned multiplication for scalar multiplication (i.e. a scalar times a vector or tensor) and for outer (or dyadic) product between two vectors (or higher order tensors). I'm not a mathematician and I came here because I needed some practical identities regarding outer product. I think it would be useful for nonmathematicians if a definition or a reference of the unsigned multiplication is given, because it is evidently not what it is usually supposed to be (neither scalar multiplication nor dyadic product). Thanks. Eratostene — Preceding unsigned comment added by Eratostene (talk • contribs) 17:56, 5 October 2011 (UTC)

Someone SHOULD merge this article

There is really no need for this article, its just a bit confusing to have a small article for something just because it has more than one name.