  Assume we are given a sum of linear measurements of $s$ different rank-$r$
matrices of the form $y = \sum_{k=1}^{s} \mathcal{A}_k ({X}_k)$. When and under
which conditions is it possible to extract (demix) the individual matrices
${X}_k$ from the single measurement vector ${y}$? And can we do the demixing
numerically efficiently? We present two computationally efficient algorithms
based on hard thresholding to solve this low rank demixing problem. We prove
that under suitable conditions these algorithms are guaranteed to converge to
the correct solution at a linear rate. We discuss applications in connection
with quantum tomography and the Internet-of-Things. Numerical simulations
demonstrate empirically the performance of the proposed algorithms.
