Talk:Rotation matrix

Introduction query

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.

Generator Question

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

What happened to Complex planes in M(2,ℝ) ?

Can't find this section anymore. I referred heavily to it 3 years ago. Thewriter006 (talk) 16:10, 9 December 2022 (UTC)

This article never said much about that 3 years ago: see for yourself. You may be thinking of the deleted article 2 × 2 real matrices (deletion discussion from February 2021) which was linked from there. –jacobolus (t) 18:28, 9 December 2022 (UTC)

To be honest that deletion decision seems pretty weak. The article (copy via the wayback machine) arguably did a poor job of contextualizing and sourcing all of its content, and was missing some of the more basic material that it should include, but nothing there was remotely "original research". Much more of that type of content – explaining various specific geometrical interpretations and uses of a common algebraic object – should be added to Wikipedia, as it can be very helpful for readers. –jacobolus (t) 19:19, 9 December 2022 (UTC)

Wikibooks has a copy:

• b:Abstract Algebra/2x2 real matrices

Some slight changes have been introduced! Rgdboer (talk) 04:06, 10 December 2022 (UTC)

Rotations as complex 2x2 matrices

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)

Symmetric Matrix Eigenvectors

> (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)

Full-stops after equations

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)

Please, don't do that, as this goes against MOS:MATH#PUNC. D.Lazard (talk) 09:00, 31 December 2023 (UTC)

Additional detail for 3D matrix multiplication and notation

Looking at the General 3D rotation case, I can’t seem to generate the same final transformation matrix as indicated. Can you show more of the details? In particular the “ij" = 12, 13, 22, & 23 matrix elements, containing many trig factors and terms, is a problem. For a R to L multiplication, you first mult the pitch matrix x the yaw matrix, right? Can you show that intermediate matrix? Then you perform roll matrix x the intermediate matrix to get the final transformation, right?. Found my error. Also applied the associative property to perform: ( roll * pitch ) * yaw.

But also, a bit confused why the angles for extrinsic are α, β, γ, about axes x, y, z ( respectively ?) while for intrinsic, they are α, β, γ, about axes z, y, x, respectively. I understand the multiplication order is reversed between intrinsic and extrinsic but the angles associated with each axis should be the same, right? Thanks. 2601:647:6480:1D20:16C:3AED:F2BB:97EF (talk) 15:51, 2 October 2024 (UTC)