Orthogonal decomposition of Lorentz transformations

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.