Talk:Givens rotation

message: How can it be that the copysign function, which copies the sign of y to x, may be replaced by x*sign(y)?
If x is negative, the result will be exactly the opposite sign of y. I suppose it should read: 
abs(x)*sign(y)
88.73.242.210 (talk) 14:31, 19 December 2007 (UTC)
replies: text: In the examples in the code, x is sqrt(1+t*t) and thus always positive. -- Jitse Niesen (talk) 23:16, 19 December 2007 (UTC)
thread_title:  Copysign 

message: What about the complex case ?  —Preceding unsigned comment added by Therealgandalf (talk • contribs) 06:19, 6 October 2008 (UTC)
thread_title:  Complex case 

message: Anybody acquainted with Geometric Algebra methods recognizes at first sight that the matrix representation of a Givens rotation does not only figure a rotation in the plane spannned by two coordinate axes, but a rotation in the whole n-dimensional space, parallel to the plane spanned by those two coordinate axes. That is expressed in GA  very simply by the bivector B_{ij}=e_i\wedge e_j, and the action on any vector is written  :
v=e^{-(\theta/2)(e_i \wedge e_j)}u e^{(\theta/2)(e_i \wedge e_j)}
where :
e^{(\theta/2)(e_i \wedge e_j)}= \cos(\theta/2)+  \sin(\theta/2) e_i \wedge e_j
In matrix representation you get the Givens matrices. That is a less easier way to describe the same operation with a lot of 1's and 0's ! But the important fact which appears in both representations is that a rotation is always represented by a plane and an angle. The fact that in R^3 we can use a rotation axis and an angle is a very particular situation. So it seems not very useful to attach a special signification to the fact that any intrinsic defined Euler angles convention can also be interpreted in extrinsic manner by matrices belonging to the Givens class ... And of course, conversely it would be incoherent with Euler angles theory to pretend that the combination of three Givens matrices cannot be interpreted in an intrinsic manner.
I suggest to reconsider the names of the different conventions in the table of composed rotations, to put them in coherence with Euler angles.I suggest also to suppress the assimilation of the subindexes with the ambiguous and here undefined denominations : intrinsic rotation, nutation, precession.
Chessfan (talk) 21:31, 15 December 2010 (UTC)
replies: text:  As I wrote before, the natural way of composing rotation operations is the "extrinsic" and I see no reason why we should use the "intrinsic" here, even if it is possible to assign a meaning for it.--Juansempere (talk) 15:06, 18 December 2010 (UTC)
thread_title: Some remarks about Givens rotations and their representations

message: The article about Jacobi rotation uses a different convention in representing the rotation matrix: the -s term is in a different place. Somebody should unify this. I personally suggest changing this article. One reason to do so is that Anderson's algorithm in fact produces the wrong sign now.  — Preceding unsigned comment added by 213.216.249.47 (talk) 15:14, 1 August 2011 (UTC)
replies: text: You are correct about the Anderson algorithm not matching the convention used elsewhere on the page, so I have corrected it (the easy way out, since changing the sign convention on s elsewhere would require numerous changes, while the algorithm only required 3). I see not compelling reason, though, to make the rotations on the Jacobi page follow the same direction as here or vice versa. The two rotations are even identified as being in opposite directions (clockwise for the Jacobi, counterclockwise here). For the main purposes of either algorithm, the direction of the rotation is of little consequence, as the rotation angle is not calculated.Eigenguy (talk) 03:39, 17 July 2012 (UTC)
thread_title:  Unifying notational conventions 

message: The "Matrix representation" section states: 
"That is, for fixed i > j, the non-zero elements of Givens matrix are given by..."
Now, looking at the matrix, g(i,j)=s for i<j NOT i>j (where I read g(i,j) to refer to 'i rows down, j columns across').  
Can someone leave a response indicating whether I'm right or wrong and, if necessary, make any changes to the page?  That is, I think the article should state: 
"That is, for fixed i < j, the non-zero elements of Givens matrix are given by..."
ASavantDude (talk) 16:30, 8 March 2018 (UTC)
thread_title:  Matrix representation section