  Maximizing a submodular function is a fundamental task in machine learning
and in this paper we study the deletion robust version of the problem under the
classic matroids constraint. Here the goal is to extract a small size summary
of the dataset that contains a high value independent set even after an
adversary deleted some elements. We present constant-factor approximation
algorithms, whose space complexity depends on the rank $k$ of the matroid and
the number $d$ of deleted elements. In the centralized setting we present a
$(4.597+O(\varepsilon))$-approximation algorithm with summary size $O(
\frac{k+d}{\varepsilon^2}\log \frac{k}{\varepsilon})$ that is improved to a
$(3.582+O(\varepsilon))$-approximation with $O(k + \frac{d}{\varepsilon^2}\log
\frac{k}{\varepsilon})$ summary size when the objective is monotone. In the
streaming setting we provide a $(9.435 + O(\varepsilon))$-approximation
algorithm with summary size and memory $O(k + \frac{d}{\varepsilon^2}\log
\frac{k}{\varepsilon})$; the approximation factor is then improved to
$(5.582+O(\varepsilon))$ in the monotone case.
