  The canonical decomposition of a Lorentz algebra element into a sum of
orthogonal simple (decomposable) Lorentz bivectors is discussed, as well as the
decomposition of a proper orthochronous Lorentz transformation into a product
of commuting Lorentz transformations, each of which is the exponential of a
simple bivector. As an application, we obtain an alternative method of deriving
the formulas for the exponential and logarithm for Lorentz transformations.
