  Explicit formulae for the $4\times 4$ Lorentz transformation matrices
corresponding to a pure boost and a pure three-dimensional rotation are very
well-known. Significantly less well-known is the explicit formula for a general
Lorentz transformation with arbitrary nonzero boost and rotation parameters. We
revisit this more general formula by presenting two different derivations. The
first derivation (which is somewhat simpler than previous ones appearing in the
literature) evaluates the exponential of a $4\times 4$ real matrix $A$, where
$A$ is a product of the diagonal matrix ${\rm diag}(+1, -1, -1, -1)$ and an
arbitrary $4\times 4$ real antisymmetric matrix. The formula for $\exp A$
depends only on the eigenvalues of $A$ and makes use of the Lagrange
interpolating polynomial. The second derivation exploits the observation that
the spinor product $\eta^\dagger\overline{\sigma}^{\lower3pt\hbox{$\scriptstyle
\mu$}}\chi$ transforms as a Lorentz four-vector, where $\chi$ and $\eta$ are
two-component spinors. The advantage of the latter derivation is that the
corresponding formula for a general Lorentz transformation $\Lambda$ reduces to
the computation of the trace of a product of $2\times 2$ matrices. Both
computations are shown to yield equivalent expressions for $\Lambda$.
