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Don't see why the 2x2 matrix given in the introduction applies to the x-y plane specifically. It applies to any 2D subspace with a defined origin/axis surely.
The rotation matrices about the x, y, and z axis do not seem to be equate to the "generator" written to their right (the rotation matrices with the matrix exponentials). It seems that one is the transpose of the other. Can someone please explain?
Thanks- James
Can't find this section anymore. I referred heavily to it 3 years ago. Thewriter006 ( talk) 16:10, 9 December 2022 (UTC)
Wikibooks has a copy:
Some slight changes have been introduced! Rgdboer ( talk) 04:06, 10 December 2022 (UTC)
Pure polarization states of light can be represented as complex 2d vectors corresponding to points on the Poincare sphere, and rotations along the surface of this sphere can be represented by complex 2x2 matrices. I find it remarkable that a point in "3D" (according to this article) can be represented by a complex 2d vector. I don't fully understand how making the vector complex produces the holonomy of a sphere, but it seems like a rather elegant way of encoding the rotation that should be included in this article. 162.246.139.210 ( talk) 19:41, 10 July 2023 (UTC)
> (Bar-Itzhack 2000) (Note: formulation of the cited article is post-multiplied, works with row vectors).
Unless I misread the matrix, the matrix in question is symmetric, and so should have left and right eigenvectors that are the same (aside from the transpose, of course). 2600:1700:3D2D:8810:5CCE:ABD5:83C0:8045 ( talk) 22:28, 3 November 2023 (UTC)
This article contains a number of full-stops and commas at the end of the equations. To me the full-stops look like a mistake in the equation. I would be inclined to either, remove them all together, or at least move them outside of the <math> tag. 217.28.11.247 ( talk) 08:42, 31 December 2023 (UTC)
This is the
talk page for discussing improvements to the
Rotation matrix article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
Archives:
1,
2,
3Auto-archiving period: 700 days
![]() |
![]() | This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
Don't see why the 2x2 matrix given in the introduction applies to the x-y plane specifically. It applies to any 2D subspace with a defined origin/axis surely.
The rotation matrices about the x, y, and z axis do not seem to be equate to the "generator" written to their right (the rotation matrices with the matrix exponentials). It seems that one is the transpose of the other. Can someone please explain?
Thanks- James
Can't find this section anymore. I referred heavily to it 3 years ago. Thewriter006 ( talk) 16:10, 9 December 2022 (UTC)
Wikibooks has a copy:
Some slight changes have been introduced! Rgdboer ( talk) 04:06, 10 December 2022 (UTC)
Pure polarization states of light can be represented as complex 2d vectors corresponding to points on the Poincare sphere, and rotations along the surface of this sphere can be represented by complex 2x2 matrices. I find it remarkable that a point in "3D" (according to this article) can be represented by a complex 2d vector. I don't fully understand how making the vector complex produces the holonomy of a sphere, but it seems like a rather elegant way of encoding the rotation that should be included in this article. 162.246.139.210 ( talk) 19:41, 10 July 2023 (UTC)
> (Bar-Itzhack 2000) (Note: formulation of the cited article is post-multiplied, works with row vectors).
Unless I misread the matrix, the matrix in question is symmetric, and so should have left and right eigenvectors that are the same (aside from the transpose, of course). 2600:1700:3D2D:8810:5CCE:ABD5:83C0:8045 ( talk) 22:28, 3 November 2023 (UTC)
This article contains a number of full-stops and commas at the end of the equations. To me the full-stops look like a mistake in the equation. I would be inclined to either, remove them all together, or at least move them outside of the <math> tag. 217.28.11.247 ( talk) 08:42, 31 December 2023 (UTC)