Multidimensional Spinors, Invariant Form, and the Dirac Equation

We have studied restrictions on the invariant form and matrix of the generalized Dirac adjoint in a space of arbitrary dimension and signature and have shown that this matrix corresponds to the fundamental symmetry of the Krein space. We have proved that the choice of the generalized Dirac adjoint matrix uniquely determines which gamma matrices correspond to the time axes and which to the space axes.