The Psigma[n] command represents the three Pauli matrices; that is, the set of Hermitian and unitary matrices:

where  is the imaginary unit (to represent it with a lowercase , see interface,imaginaryunit). Together with , representing the 2 x 2 identity matrix, the Pauli matrices form an orthogonal basis. The  matrices are displayed as .

When multiplied by the imaginary unit, these matrices are a realization of the Lie algebra of the SU(2) group, which is isomorphic to the Lie algebra of SO(3). So, the  are also a matrix realization of infinitesimal rotations in 3D space, hence serving as representation for the 3D angular momentum operator in Physics.

The Pauli matrices satisfy the commutation relations , where  is the Levi-Civita symbol, and  range from 1 to 3. The  also satisfy the anticommutation relations , where  is the Kronecker delta. Those two relations can be written as .

For  from 1 to 3, the Pauli matrices satisfy , and  (the 2 x 2 identity matrix), where Det represents the determinant, and Trace represents/computes the trace. In the context of the Physics package (see conventions), you can also use the index 0, as in , and it will be automatically mapped into .