These matrices are traceless, Hermitian (so they can generate unitary matrix group elements through exponentiation), and obey the extra trace orthonormality relation. These properties were chosen by Gell-Mann because they then naturally generalize the Pauli matrices for SU(2) to SU(3), which formed the basis for Gell-Mann's quark model.Gell-Mann's generalization further extends to general SU().

linear algebra - Traceless matrix - Mathematics Stack Exchange Any matrix is similar to its Jordan form, which is upper triangular. From this points of view, the only information that you get from the matrix being traceless is that the sum of the eigenvalues is zero. From another point of view, it is well known that any trace-zero matrix is a commutator, i.e… Physics 251 Propertiesof theGell-Mann matrices Spring 2011 Physics 251 Propertiesof theGell-Mann matrices Spring 2011 The Gell-Mann matrices are the traceless hermitian generators of the Lie algebra su(3), analogous to the Pauli matrices of su(2). The eight Gell-Mann matrices are deﬁned by: λ 1 = 0 1 0 1 0 0 0 0 0 , λ 2 = 0 −i 0 i 0 0 0 0 0 , λ 3 = 1 0 0 0 −1 0 0 0 0 , λ 4 = Traceless tensors and the symmetric group - ScienceDirect Nov 01, 1979

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Physics 251 Propertiesof theGell-Mann matrices Spring 2011 The Gell-Mann matrices are the traceless hermitian generators of the Lie algebra su(3), analogous to the Pauli matrices of su(2). The eight Gell-Mann matrices are deﬁned by: λ 1 = 0 1 0 1 0 0 0 0 0 , λ 2 = 0 −i 0 i 0 0 0 0 0 , λ 3 = 1 0 0 0 −1 0 0 0 0 , λ 4 = Traceless tensors and the symmetric group - ScienceDirect Nov 01, 1979 PAULI MATRICES: PROPERTIES Principles of Quantum …

### Pauli matrices - Wikipedia

real traceless symmetric matrix in source free region. s. The method for obtaining the eigenvalues of a general 3 × 3 general matrix involves finding the roots of a third order polynomial and has been known for a long time. Pedersen and Rasmussen (1990) exhibit the solutions for our case. Interpreting the eigenvalues has proven to be an