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![]() | The contents of the Shear matrix page were merged into Shear mapping on 21 December 2023. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
Shear preserves all parallel lines as being parallel -- what is the name for a transform does not do this, turning a square into a trapezoid?
I propose that this article and shear matrix be merged. Though that article was created with only two edits, it is a valuable resource on this topic. Only today did I learn of it and respond to the alert given by another editor. On the other hand, that article uses column vectors, instead of the in-line row vector approach. Since linear algebra depends on facility with both, this jump between pages gives some necessary exercise. Futhermore, the focus on two-dimensions at the outset, allows this article to be more introductory. In that view, the "fixed subspace form" section belongs more with shear matrix. Rgdboer 20:24, 4 September 2007 (UTC)
Today I made the move and repaired most links in WP. If you find a reference to the old name, you're home now. The issue of row vector versus column vector continues to stand in the way of a merger with shear matrix; the value of ambidexterity being noted. Rgdboer 02:37, 14 November 2007 (UTC)
Someone using computer 147 94 187 222 located on cote d'azure near Marseille edited this page on 14 October 2008. The edit changed the matrix applications to column vectors. The editor is unidentified and gave no reason for the change; furthermore, there was some loss of sense in the text with the change. Today row vectors have been re-instated. Rgdboer ( talk) 01:10, 20 January 2009 (UTC)
In the case of a shear parallel to the x-axis, the matrix is and a shear parallel to the y-axis therefore has the matrix .
This has been corrected :)
(Reference:
http://store.aqa.org.uk/qual/pdf/AQA-MFP4-TEXTBOOK.PDF page 18)
Jambo6c (
talk)
Further to the instincts of 147.94.187.222 and Jambo6c ( talk · contribs) above, I'm changing the article from using row vectors to using column vectors.
A couple of reasons might be hypothesised for this:
For these reasons, it makes more sense for the exposition here to use column vectors, rather than the mathematically equivalent row vector forms. Jheald ( talk) 08:19, 19 May 2009 (UTC)
Can I suggest maybe we seek additional third-party input? Silly rabbit ( talk · contribs) and Geometry guy ( talk · contribs) both have judgment I'd respect. Jheald ( talk) 21:29, 22 May 2009 (UTC)
What in this article is called the "elementary" version of the shear mapping ought to be called the false version, since it is not a correct definition.
What is called the "advanced" version is the correct definition.
Instead of including a wrong definition, why not break the article up in the following way: 1) the 2-dimensional case, and 2) the n-dimensional case (n >= 2). (Actually, the n-dimensional version is valid, but trivially, in the 1-dimensional case as well.
(What is false about what the article calls the elementary version is that in an actual shear transformation, there is nothing whatsoever saying that the fixed subspace need be parallel to an axis.) Daqu ( talk) 10:24, 26 November 2009 (UTC)
Does ML's nose really need to be picked in an article about math? —Preceding unsigned comment added by 112.200.186.149 ( talk) 12:30, 15 April 2011 (UTC)
The following was removed today:
Such deception is to be deplored in this project. Rgdboer ( talk) 01:12, 28 January 2015 (UTC)
Regarding the following:
I think it would be more accurate to describe oblique, not "italic", type as having been sheared, as true italic type uses unique glyphs not producible by shearing. See Italic_type#Oblique_type_compared_to_italics. Oblique type is often used as a surrogate for italic when italic glyphs are unavailable. Iddr ( talk) 09:54, 6 April 2016 (UTC)
The current description in the article would suggest that this is a horizontal shear. But the image name and description call it vertical. Is there some ambiguity here? Otherwise I would request to rename the image (and my derivate of it). Watchduck ( quack) 00:27, 8 July 2022 (UTC)
This was suggested more than 15 years ago by Rgdboer, and I think it was correct: there is not a true separation in the study of the two objects, they are just two manifestations of a common thing. To the extent that there are matrix-specific things to say (e.g., concerning elementary matrices) I don't see why they can't fit into a single article (neither one is very long). JBL ( talk) 18:39, 23 May 2023 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
![]() | The contents of the Shear matrix page were merged into Shear mapping on 21 December 2023. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
Shear preserves all parallel lines as being parallel -- what is the name for a transform does not do this, turning a square into a trapezoid?
I propose that this article and shear matrix be merged. Though that article was created with only two edits, it is a valuable resource on this topic. Only today did I learn of it and respond to the alert given by another editor. On the other hand, that article uses column vectors, instead of the in-line row vector approach. Since linear algebra depends on facility with both, this jump between pages gives some necessary exercise. Futhermore, the focus on two-dimensions at the outset, allows this article to be more introductory. In that view, the "fixed subspace form" section belongs more with shear matrix. Rgdboer 20:24, 4 September 2007 (UTC)
Today I made the move and repaired most links in WP. If you find a reference to the old name, you're home now. The issue of row vector versus column vector continues to stand in the way of a merger with shear matrix; the value of ambidexterity being noted. Rgdboer 02:37, 14 November 2007 (UTC)
Someone using computer 147 94 187 222 located on cote d'azure near Marseille edited this page on 14 October 2008. The edit changed the matrix applications to column vectors. The editor is unidentified and gave no reason for the change; furthermore, there was some loss of sense in the text with the change. Today row vectors have been re-instated. Rgdboer ( talk) 01:10, 20 January 2009 (UTC)
In the case of a shear parallel to the x-axis, the matrix is and a shear parallel to the y-axis therefore has the matrix .
This has been corrected :)
(Reference:
http://store.aqa.org.uk/qual/pdf/AQA-MFP4-TEXTBOOK.PDF page 18)
Jambo6c (
talk)
Further to the instincts of 147.94.187.222 and Jambo6c ( talk · contribs) above, I'm changing the article from using row vectors to using column vectors.
A couple of reasons might be hypothesised for this:
For these reasons, it makes more sense for the exposition here to use column vectors, rather than the mathematically equivalent row vector forms. Jheald ( talk) 08:19, 19 May 2009 (UTC)
Can I suggest maybe we seek additional third-party input? Silly rabbit ( talk · contribs) and Geometry guy ( talk · contribs) both have judgment I'd respect. Jheald ( talk) 21:29, 22 May 2009 (UTC)
What in this article is called the "elementary" version of the shear mapping ought to be called the false version, since it is not a correct definition.
What is called the "advanced" version is the correct definition.
Instead of including a wrong definition, why not break the article up in the following way: 1) the 2-dimensional case, and 2) the n-dimensional case (n >= 2). (Actually, the n-dimensional version is valid, but trivially, in the 1-dimensional case as well.
(What is false about what the article calls the elementary version is that in an actual shear transformation, there is nothing whatsoever saying that the fixed subspace need be parallel to an axis.) Daqu ( talk) 10:24, 26 November 2009 (UTC)
Does ML's nose really need to be picked in an article about math? —Preceding unsigned comment added by 112.200.186.149 ( talk) 12:30, 15 April 2011 (UTC)
The following was removed today:
Such deception is to be deplored in this project. Rgdboer ( talk) 01:12, 28 January 2015 (UTC)
Regarding the following:
I think it would be more accurate to describe oblique, not "italic", type as having been sheared, as true italic type uses unique glyphs not producible by shearing. See Italic_type#Oblique_type_compared_to_italics. Oblique type is often used as a surrogate for italic when italic glyphs are unavailable. Iddr ( talk) 09:54, 6 April 2016 (UTC)
The current description in the article would suggest that this is a horizontal shear. But the image name and description call it vertical. Is there some ambiguity here? Otherwise I would request to rename the image (and my derivate of it). Watchduck ( quack) 00:27, 8 July 2022 (UTC)
This was suggested more than 15 years ago by Rgdboer, and I think it was correct: there is not a true separation in the study of the two objects, they are just two manifestations of a common thing. To the extent that there are matrix-specific things to say (e.g., concerning elementary matrices) I don't see why they can't fit into a single article (neither one is very long). JBL ( talk) 18:39, 23 May 2023 (UTC)