Unified Representation of 3D Multivectors with Pauli Algebra in Rectangular, Cylindrical and Spherical Coordinate Systems

In practical engineering, the use of Pauli algebra can provide a computational advantage, transforming conventional vector to straightforward matrix manipulations. this work, matrices in cylindrical and spherical coordinates are reported for first time their representing three-dimensional is discussed. This method leads unified representation 3D multivectors with algebra. A significant advantage that approach provides independent coordinate system, which does not exist perspective. Additionally, representations nabla operator different systems derived Finally, an example on radiation from dipole given illustrate advantages methodology.