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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
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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
Knowledge articles should be written to reflect sources, not idiosyncratic whims of a single editor. Of
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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
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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
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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
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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
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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
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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
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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
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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.
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411:{\displaystyle \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}}}
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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.
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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
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preferred. Any effort to provide for a right-to-left matrix and vector process would require modification of the fundamental row x column convention. —
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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
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elements. Without proper justification this was changed into the present formulation. Can someone explain to me what a "column of entries" is?
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I tried too much to find the geometry of determinate adjoint inverse row and column vector but still I'm hopeless please explain it
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matrix, but there are also sources which hink that just writing entries top down in a column, produces a column vector.
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Deleted. If you want to reinsert, please add a reliable reference or specify the context in which the notation is used.
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670:{\displaystyle {\begin{bmatrix}x\\y\\z\end{bmatrix}}\quad {\text{or}}\quad {\begin{bmatrix}x&y&z\end{bmatrix}}}
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says: "Matrices with a single row are called row vectors, and those with a single column are called column vectors."
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on topic questions like the one you ask. Talk pages are for questions/answers/discussions on improving the article.
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The discussion here is about some changes to the lead, but they were part of some much broader changes -- see
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September 2015. For the contribution history and old versions of the redirected page, please see
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Also, that claim had no reference and seems like it would be very difficult to source reliably. --
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for that content in the latter page, and it must not be deleted as long as the latter page exists.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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rewrote the lead sentences and it now (again) includes the interpretation you prefer.
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1384:@
1358::
1354:@
1333:(
1315:(
1309:m
1301:m
1277:(
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1190:1
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1149:)
1144:1
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1091:,
1086:1
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1076:1
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1068:(
1065:(
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946:k
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851:n
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820:(
804:(
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794:A
763:(
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719:И
715:ε
713:ħ
710:c
704:Ŝ
702:∧
697:M
663:]
657:z
652:y
647:x
641:[
625:]
619:z
612:y
605:x
599:[
551:z
546:e
541:z
538:+
533:y
528:e
523:y
520:+
515:x
510:e
505:x
502:=
498:r
464:(
445:(
431:(
422:(
404:]
396:m
392:x
388:,
382:,
377:2
373:x
369:,
364:1
360:x
353:[
348:=
342:T
336:x
327:]
319:m
315:x
302:2
298:x
290:1
286:x
279:[
274:=
270:x
245:(
229:.
143:.
42::
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