Kvaterniooni

Kvaterniooni is a mathematical concept that extends complex numbers. While complex numbers have a real part and an imaginary part represented by 'i', where i squared equals -1, quaternions introduce two additional imaginary units, 'j' and 'k'. A quaternion can be written in the form a + bi + cj + dk, where a, b, c, and d are real numbers. The multiplication rules for these units are: i squared = j squared = k squared = ijk = -1, and also ij = k, ji = -k, jk = i, kj = -i, ki = j, ik = -j.

This system of multiplication is non-commutative, meaning the order of multiplication matters, unlike with real or complex numbers. Quaternions were invented by William Rowan Hamilton in 1843. They are useful in various fields, particularly in representing rotations in three-dimensional space. Because they avoid the gimbal lock problem that can affect other rotation representations, they are widely used in computer graphics, robotics, and aerospace engineering.

The algebra of quaternions is a four-dimensional division algebra over the real numbers. This means that every non-zero quaternion has a multiplicative inverse. Applications of quaternions include interpolating between orientations, which is crucial for smooth animation in computer graphics.