Vectors

For a Skew-Hermitian matrix, eigenvalues are purely imaginary. The only real eigenvalue possible is .

The behavior of the unit vectors under inversion (reflection through the origin) can be determined as follows:
- In spherical coordinates, the position vector is given by:
- Under inversion , the radial unit vector transforms as:
- The polar unit vector is defined as:
- Since changes sign under inversion, its derivative with respect to remains unchanged.
- Therefore, has even parity.
- The azimuthal unit vector is defined as:
- Since changes sign under inversion, its derivative with respect to also changes sign.
- Hence, has odd parity.