Thanks Gareth. It does indeed sound like a "Givens rotation" is the term I was looking for for what I was calling a "primitive rotation". Tom Gareth McCaughan writes:
On 12/03/2016 00:15, Tom Karzes wrote:
I have a question about a particular type of decomposition of N-dimensional rotation matrices. The specific types of matrices I am considering are orthogonal matrices (the rows form a set of orthogonal unit vectors, as do the columns). Further, I am only considering the case where the determinant is 1 (as opposed to -1). I.e., I am disallowing reflections.
I am interested in factoring such a matrix into a sequence of "primitive rotations" (I'm not sure what the proper term is). By this I mean rotations which only affect two coordinate axes. This defines a rotation within a plane, with the restriction that the plane be the product of two of the standard coordinate axes.
The usual term is "Givens rotation".
(I don't know the answer to your question about what orderings of axis-pairs "work".)
-- g
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