  The Kaczmarz algorithm (KA) is a popular method for solving a system of
linear equations. In this note we derive a new exponential convergence result
for the KA. The key allowing us to establish the new result is to rewrite the
KA in such a way that its solution path can be interpreted as the output from a
particular dynamical system. The asymptotic stability results of the
corresponding dynamical system can then be leveraged to prove exponential
convergence of the KA. The new bound is also compared to existing bounds.
