  The classical Kaczmarz iteration and its randomized variants are popular
tools for fast inversion of linear overdetermined systems. This method extends
naturally to the setting of the phase retrieval problem via substituting at
each iteration the phase of any measurement of the available approximate
solution for the unknown phase of the measurement of the true solution. Despite
the simplicity of the method, rigorous convergence guarantees that are
available for the classical linear setting have not been established so far for
the phase retrieval setting. In this short note, we provide a convergence
result for the randomized Kaczmarz method for phase retrieval in
$\mathbb{R}^d$. We show that with high probability a random measurement system
of size $m \asymp d$ will be admissible for this method in the sense that
convergence in the mean square sense is guaranteed with any prescribed
probability. The convergence is exponential and comparable to the linear
setting.
