Quaternions have a matrix representation in which the sum and product of quaternions correspond to the sum and product of the representing matrices, and the determinant of the matrix is the square of the represented quaternion's magnitude. Using conventional mathematical notation with a_i for a sub i and z* for z conjugate, the quaternion
a_0 + a_1 i + b_0 j + b_1 k is represented by the matrix a b -b* a* where a is a_0 + a_1 i and b is b_0 + b_1 i . I recommend using this representation when you want to deal with quaternions in J. (For proofs it helps to know a_0 + a_1 i + b_0 j + b_1 k is a_0 + a_1 i + b_0 j + b_1 i j which is a_0 + a_1 i + (b_0 + b_1 i) j that is a + b j where a and b are the complex numbers given above. See equation (61) in Ch VIII Section 10 of Birkhoff and Mac Lane, A Survey of Modern Algebra, Revised Edition, Macmillan 1953. ) Kip Raul Miller wrote: > On Sun, Mar 14, 2010 at 7:18 AM, Dan Bron <[email protected]> wrote: >> b. Quaternions :) > > I made a proposal for quaternions some time ago in the wiki. > > But I was not certain about how to handle some efficiency > issues. In retrospect, efficiency issues should probably > be ignored. > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
