kvaternione
Kvaternione are a number system that extends the complex numbers by adding three imaginary units. A quaternion is written as q = a + bi + cj + dk, with a, b, c, d real and i^2 = j^2 = k^2 = ijk = -1. The set H of quaternions forms a non-commutative, associative division algebra over the reals.
Quaternions can be represented as q = (a, u) where a ∈ R and u ∈ R^3. For p =
Conjugate q* = a - u and norm N(q) = a^2 + ||u||^2. If q ≠ 0, the inverse is q^{-1}
Unit quaternions provide a representation of 3D rotations. A rotation by q maps a vector v to
Historically, quaternions were invented by William Rowan Hamilton in 1843 as a four-dimensional generalization of complex
Quaternions also have matrix representations, linking them to 4×4 real or 2×2 complex matrices. This dual view