personal notes of Renzo Diomedi
, then if n=3 =
,
properties:
and
and
, , , , the reciprocal of a is b and vice versa
then
, ,
,
=
its conjugate = its transpose
where ~ is the equivalence relation that identifies 2 points
if they both lie on the same straight line passing through the origin
dot and cross prod.:
unit vector, rot.axis
where is parallel and is perpendicular to rotation axis
=1/4(-a-b-c+ai+ak+aj+bj+bk+bi+ck-cj+ci+ai+bi+ci+a+aj+ak+bk+bj-b-cj-ck+c+aj+bj+cj-ak-ai+a+b+bi+bk+ci-c-ck+ak+bk+ck+aj-a-ai-bi+b-bj+c+ci+cj)=
length =
unit q =
a 2PI/3 rotation permutes i,j,k
and rot.func.= 3 axes are permutated ciclically
geodesic eq.
..............................to be continued
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