Talk:Collinearity

Headline text
The net is redirecting the searched contents to a more basic meaning. 141.214.17.17 (talk) 21:08, 7 August 2008 (UTC)

Colinear maps
Colinear maps have nothing im common with collinearity. It is a mere syntactic resemblence. --Tillmo (talk) 16:10, 2 March 2009 (UTC)

Talk of spelling and Latin grammatical rules
How is this relevant to a largely-mathematical concept? Just saying "Collinearity (also co-linearity and colinearity)" would be sufficient, if you REALLY wanted people to know about the alternative spellings. —Preceding unsigned comment added by 72.248.107.194 (talk) 19:55, 1 May 2009 (UTC)

Reason for reverting
The above comment is a good example of why more needs to be said than just common misspellings. There are many readers who think that the one "l" version of the term is an alternate spelling and are unaware that that spelling changes the meaning. In this day and age, when correct spelling is not considered a high priority, it is important to point out changes in meaning that can occur in this way. Perhaps the phrasing could be improved, but I definitely think that something needs to be said. As to the redundancy ... a little bit of it doesn't hurt the article, especially considering that it is a disambiguation page with readers coming to it with different mindsets as to what the term means. Furthermore, even if this was some terrible violation of Wiki "rules", the wrong one was eliminated. Bill Cherowitzo (talk) 05:34, 7 February 2012 (UTC)


 * I too thought (until a moment ago) that colinear is a misspelling, and I'm not aware of any different meaning of colinear. I just looked it up in Wiktionary, and found that Wiktionary claims that colinear is an alternative spelling of collinear, with no separate definition given. Random House Webster's College Dictionary agrees.


 * Do you have evidence that some authority considers colinear to be an incorrect spelling? And, what changed meaning do you say is attached to colinear?


 * As for the redundancy, there's simply no reason to say the same thing twice in a row; there's simply no reason to say the same thing twice in a row--it makes the disambiguation page look sloppy. And it is standard practice on disambiguation pages to put the primary usage in the opening sentence, separating it from the less common uses; so I think I deleted the right one. Duoduoduo (talk) 17:16, 7 February 2012 (UTC)

The word "colinear" refers to the dual of linear in certain algebraic contexts, as is pointed out on this disambiguation page. Your finding the term in general dictionarys just points out the problem that mathematical terms are just not treated accurately in those venues (and there is absolutely no reason to trust Wiktionary or any similar on-line source). Asking for an authority for an incorrect spelling is a red herring, how many authorities can you find that will say that "fisch" is a misspelling of the aquatic animal. There are no geometry texts that spell collinear with one "l" that I am aware of, I consider that to be the real authority on this issue. Bill Cherowitzo (talk) 23:19, 7 February 2012 (UTC)

And on the redundancy issue, while I certainly agree that a primary usage ought to appear in an opening sentence, there are no rigid rules about that ... and for emphasis I repeat, THERE ARE NO RIGID RULES ABOUT THAT! Even if there were, I would stand by WP:IAR and claim that the page is actually better off (clearer and less awkward) with this little bit of redundancy. Bill Cherowitzo (talk) 05:10, 8 February 2012 (UTC)

Revert in the lead
I've pulled the following sentence from the lead,


 * The term collinear has also been used elsewhere in mathematics and in its application areas, as a reference to concepts of line and linear dependence.

because I don't consider it to be correct (or at the least misleading). The term is not referring to a property of lines, nor an intrinsic property of points - it is a property of flags (the incidence relation). To refer just to lines (or just to points) is only telling half of the story. Linear dependence is an algebraic property. In order to bring collinearity into the picture you must be interpreting the situation in geometric terms. In general, this is not a natural way to view the algebraic relation. I don't remember seeing the term raised in any discussion of linear dependence. Of course some good references may correct this impression, but it would still be a stretch and I am not sure that it belongs in the lead. Perhaps if there were some mention of the connection in the article this could be justified. Bill Cherowitzo (talk) 18:52, 6 May 2013 (UTC)

Matrix formulation: accurate?
It's likely that I'm just confused about this, but the following section seems inaccurate:
 * In coordinate geometry, in n-dimensional space, a set of three or more distinct points are collinear if and only if, the matrix of the coordinates of these vectors is of rank 1 or less. For example, given three points X = (x1,&#8239;x2,&#8239;...&#8239;,&#8239;xn), Y = (y1,&#8239;y2,&#8239;...&#8239;,&#8239;yn), and Z = (z1,&#8239;z2,&#8239;...&#8239;,&#8239;zn),  if the matrix
 * $$\begin{bmatrix}

x_1 & x_2 & \dots & x_n \\ y_1 & y_2 & \dots & y_n \\ z_1 & z_2 & \dots & z_n \end{bmatrix} $$
 * is of rank 1 or less, the points are collinear.

IIRC, rank is just a measure of linear independence. But points need not be linearly dependent to be collinear. For example, the following points are all on the 2D line y = 1, but their coordinates are linearly independent: (1, 1), (2, 1), (3, 1). The matrix representation is:


 * $$\begin{bmatrix}

1 & 1 \\ 2 & 1 \\ 3 & 1 \end{bmatrix} $$

which is of rank 2. I suspect that rank is actually a measure of collinearity only for lines that run through the coordinate origin.

The determinant formulation seems to be accurate.

NillaGoon (talk) 22:10, 4 June 2020 (UTC)