Abstract
We obtain the canonical forms which define the classes of the full Lorentz group inn-dimensions. Besides the forms expected by analogy with the orthogonal group, which can be reduced to the diagonal form in the field of complex numbers, there exists a canonical form whose first component matrix is the matrix ±exp.r o given by (7) in Section 6. This 3×3 matrix characterizes a class of Lorentz matrices with equal eigenvalues, +1 or −1, which cannot be diagonalized even in the field of complex numbers.
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