reasons:
- in general, it's not actually easier to interpolate rotors compared to matrices
- matrices are better-studied so it's easier to find algorithms
- matrices scale better in high dimensions (rotors win in 6D and below; matrices win in 7D and above)
distance(A, B) = entrywise dot product
Notes (from things Milo was saying)
entrywise dot product of A and B = trace(A BH)
(BH = conjugate transpose of B)
for unitary matrices, BH = B^-1
trace = sum of diagonal = sum of eigenvalues
reasons:
distance(A, B) = entrywise dot product
Notes (from things Milo was saying)
entrywise dot product of A and B = trace(A BH)
(BH = conjugate transpose of B)
for unitary matrices, BH = B^-1
trace = sum of diagonal = sum of eigenvalues