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Rotating a set of vertices
Posted:
May 9, 2010 1:55 PM


Hi All,
I have a set of 'm' *unit* vectors, v1, v2, ... vm, with k dimensions each.
The angle between any two vectors is less than 90 degrees, by that I mean that the dot/inner product of any two vectors is positive, vi.vj >= 0 forall i,j in [1, m]
Now since all the angles between the vectors are less than 90 degrees, they can all 'fit' in one quadrant (quadrant/octant ... by quadrant i mean a region in the kdimensional space where all the j^th coordinates of all the 'm' vectors have the same sign, forall j's) .
The problem is to find one such rotation matrix U such that all U*vi forall i, are in the *first quadrant*.
It suffices to give a transformation matrix to transform the set of vectors into *any* quadrant, and then we can have a set of reflections to bring them into the *first quadrant* (just change all the negative coordinates enmasse to positive).



