Talk:Row and column vectors

I notice in beginning of the "Notation" section, that the transposed notation and its alternative are exactly the same. Someone who knows the correct notations should edit it. —Preceding unsigned comment added by 75.173.43.85 (talk) 10:42, 14 May 2010 (UTC)

References about questionable alternative notation

$\mathbf {x} ={\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}\qquad \mathbf {x} ^{\rm {T}}={\begin{bmatrix}x_{1},x_{2},\dots ,x_{m}\end{bmatrix}}$

Are we sure that this (IMO questionable) alternative notation is conventionally used in some context? What context? Please give references. The history page shows that the text about alternative notation was inserted by an anonymous newbie (164.107.166.97)
Paolo.dL (talk) 14:05, 8 June 2008 (UTC)

Deleted. If you want to reinsert, please add a reliable reference or specify the context in which the notation is used. Paolo.dL (talk) 15:29, 10 June 2008 (UTC)

geometrical meaning of row and column vectors

I tried too much to find the geometry of determinate adjoint inverse row and column vector but still I'm hopeless please explain it Muzammalsafdar (talk) 14:33, 15 April 2016 (UTC)

They have no literal geometric meaning, they are just arrays of numbers. Still, in geometry they are used as a way to arrange the components of a Euclidean vector, for example the position vector in the Cartesian basis

$\mathbf {r} =x\mathbf {e} _{x}+y\mathbf {e} _{y}+z\mathbf {e} _{z}$

could be abbreviated by just specifying the coordinates of the vector as a tuple, (x, y, z), or as a row/column vector

${\begin{bmatrix}x\\y\\z\end{bmatrix}}\quad {\text{or}}\quad {\begin{bmatrix}x&y&z\end{bmatrix}}$

since the Cartesian basis is assumed. The transpose does not correspond to anything geometrically significant (although some people use the column for a vector, and the transpose for the corresponding dual vector). Hope this helps.

By the way, some editors will point you to the WP:reference desk on topic questions like the one you ask. Talk pages are for questions/answers/discussions on improving the article. M∧Ŝc²ħεИ_τlk 16:23, 15 April 2016 (UTC)

Right-to-left script

Matrix multiplication is a writing system based on left-to-right reading. An editor mentioned that the use of column vectors as input for matrix transformation may appeal to readers of a right-to-left writing system. Since composed matrix transformations should concur with matrix multiplication, the article argues that row vectors are preferred. Any effort to provide for a right-to-left matrix and vector process would require modification of the fundamental row x column convention. — Rgdboer (talk) 23:16, 29 March 2018 (UTC)

Also, that claim had no reference and seems like it would be very difficult to source reliably. --JBL (talk) 23:26, 29 March 2018 (UTC)

Preferred input vectors for matrix transformations

The section Row and column vectors#Preferred input vectors for matrix transformations violates WP:NPOV by including only carefully chosen references that go against the much more common practice in linear algebra books and elsewhere of having matrices act as functions on the left on column vectors. Of course the right action on row vectors has the advantage that to act by AB one acts first by A and then by B, but that is not the commonly used action of matrices on vectors because it has the major disadvantage of being backwards from the way function composition is standardly written. Ebony Jackson (talk) 23:54, 18 February 2021 (UTC)

This all is superfluous as a column vector is a nx1 matrix, and not an input vector for matrix transformations. The product of the mxn matrix A and the coliumn vector v is just Av and results in a mx1 column vector. The product of the 1xn row vector v and the nxm matrix A and is just vA a 1xm row vector.Madyno (talk) 18:11, 3 December 2022 (UTC)

Definition

The article says: a column vector is a column of entries. Actually, I don't know what a column of entries is. As far as I know, in linear algebra, there is no concept of a column as such. Thr only occurrence is a column in a $n\times n$ matrix, being one of the $n\times 1$ matrices $(a_{1k},a_{2k},\ldots ,a_{nk})$. In my opinion a column vector is formally a $n\times 1$ matrix, or a n-tuple of n 1-tuples: $(a_{11},a_{21},\ldots ,a_{n1})$, or $((a_{1})_{1},(a_{2})_{1},\ldots ,(a_{n})_{1})$. Madyno (talk) 14:02, 29 November 2022 (UTC)

I am having trouble telling if this comment is serious. An $n\times 1$ matrix is "a column of entries". If you want to think of that as a definition of the phrase "a column of entries" instead of as a triviality of naming, I guess you are welcome to do so, but Wikipedia articles should be written to reflect sources, not idiosyncratic whims of a single editor. Of course I would be open to discussion of individual changes, but broadly I agree with MarkH21's edit and explanation from last year. JBL (talk) 17:42, 30 November 2022 (UTC)

If a column of entries is a $n\times 1$ matrix then why not say so. Several edits ago, this was done, but for some reason this formulation has been removed. And by the way, there are plenty sources that define a column vector as a $n\times 1$ matrix, but there are also sources which hink that just writing entries top down in a column, produces a column vector. Madyno (talk) 20:50, 30 November 2022 (UTC)

Till 19 February 2021 the intro reads: In linear algebra, a column vector or column matrix is an m × 1 matrix, that is, a matrix consisting of a single column of m elements. Without proper justification this was changed into the present formulation. Can someone explain to me what a "column of entries" is? Madyno (talk) 18:27, 3 December 2022 (UTC)

In the article matrix (mathematics) it says: "Matrices with a single row are called row vectors, and those with a single column are called column vectors." and this should be written also in this article. Madyno (talk) 10:36, 4 December 2022 (UTC)

Preferred input vectors for matrix

@JayBeeEll: This discussion appears to be about the lead, but I don't think my edits from last year touched that? — MarkH₂₁^talk 22:27, 30 November 2022 (UTC)

@MarkH21: The discussion here is about some changes to the lead, but they were part of some much broader changes -- see [1] and [2]. JBL (talk) 22:29, 30 November 2022 (UTC)

Ah I see, thanks. Yes I still stand by the reasoning of my edit and the several other editors who have expressed similar opinions in the talk pages mentioned in my edit summary. There was consensus to remove the (largely original research) content. — MarkH₂₁^talk 06:01, 1 December 2022 (UTC)

Disputed

See also the discussion above. The concept 'column' doesn't exist in linear algebra, so a definition can't be given with this term. Furthermore: the article matrix (mathematics) says: "Matrices with a single row are called row vectors, and those with a single column are called column vectors." Madyno (talk) 09:22, 6 December 2022 (UTC)

While you have been talking to yourself here, Ebony Jackson rewrote the lead sentences and it now (again) includes the interpretation you prefer. JBL (talk) 18:23, 6 December 2022 (UTC)

Why this hostile tone?Madyno (talk) 13:05, 7 December 2022 (UTC)