flash said:
flash said:
Quaternions are a four-dimensional extension of complex numbers that are used to represent rotations and orientations in three-dimensional space.
To multiply quaternions, you use the formula (a + bi + cj + dk)(x + yi + zj + wk) = (ax - by - cz - dw) + (aw + bx + cy - dz)i + (az - bw + cx + dy)j + (ay + bz + cw + dx)k. Essentially, you distribute and combine like terms as you would with regular algebraic multiplication.
Quaternion multiplication is significant because it allows for easy and efficient representation of 3D rotations and orientations. It is also useful in fields such as computer graphics, robotics, and physics.
Quaternion multiplication differs from regular multiplication in that it is non-commutative, meaning that the order in which the quaternions are multiplied matters. It is also non-associative, meaning that the grouping of the quaternions can affect the result.
Technically, quaternions can be divided, but it is not a common operation and is not as straightforward as multiplication. Division of quaternions is also not commutative or associative, and the result may not always be a valid quaternion.