Gell-Mann matrices [SEP] named after
eight formula_21 are real numbers and a sum over the index is implied. Given one representation, an equivalent one may be obtained by an arbitrary unitary similarity transformation, since that leaves the commutator unchanged.
The matrices can be realized as a representation of the infinitesimal generators of the special unitary group called SU(3). The Lie algebra of this group (a real Lie algebra in fact) has dimension eight and therefore it has some set with eight linearly independent generators, which can be written as formula_22, with "i"
Generalizations of Pauli matrices
In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few classes of such matrices are summarized.
Generalized Gell-Mann matrices (Hermitian).
Generalized Gell-Mann matrices (Hermitian) Construction.
Let be the matrix with 1 in the -th entry and 0 elsewhere. Consider the space of "d"×"d" complex matrices, , for a fixed "d"