SetDirectory["/www/user/fdahl/papers/Conjugation/"];
<<kappaLib.m

Table[emOrd[i],{i,1,6}]

Hodge of Euclidean metric (++++)

metric = DiagonalMatrix[{1,1,1,1}];
kappa=emHodge[metric];
matrix =emKappaToMatrix[kappa];
matrix//MatrixForm
Eigenvalues[matrix]

Hodge of Lorentz metric (-+++)

metric = DiagonalMatrix[{-1,1,1,1}];
kappa=emHodge[metric];
matrix = emKappaToMatrix[kappa];
matrix//MatrixForm
Eigenvalues[matrix]

Hodge of indefinite metric (--++)

metric = DiagonalMatrix[{-1,-1,1,1}];
kappa=emHodge[metric];
matrix =emKappaToMatrix[kappa];
matrix//MatrixForm
Eigenvalues[matrix]

Hodge of indefinite metric (+--+)

metric = DiagonalMatrix[{1,-1,-1,1}];
kappa=emHodge[metric];
matrix =emKappaToMatrix[kappa];
matrix//MatrixForm
Eigenvalues[matrix]

6x6 matrix in Appendix A

m=(({{0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}}));

Eigenvalues[m]