Gell-Mann Matrices

Author

Eric W. Weisstein
May 24, 2024

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/Gell-MannMatrices.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Gell-MannMatrices.html.

©2024 Wolfram Research, Inc. except for portions noted otherwise

Matrices

GellMannMatrices={(({{0, 1, 0}, {1, 0, 0}, {0, 0, 0}})),(({{0, -I, 0}, {I, 0, 0}, {0, 0, 0}})),(({{1, 0, 0}, {0, -1, 0}, {0, 0, 0}})),(({{0, 0, 1}, {0, 0, 0}, {1, 0, 0}})),(({{0, 0, -I}, {0, 0, 0}, {I, 0, 0}})),(({{0, 0, 0}, {0, 0, 1}, {0, 1, 0}})),(({{0, 0, 0}, {0, 0, -I}, {0, I, 0}})),(1/(Sqrt[3]))(({{1, 0, 0}, {0, 1, 0}, {0, 0, -2}}))};

GellMannMatrices//ColumnForm//TraditionalForm

Tr/@GellMannMatrices

HermitianMatrixQ/@GellMannMatrices

Table[Tr[GellMannMatrices[[i]].GellMannMatrices[[j]]]==2KroneckerDelta[i,j],{i,8},{j,8}]