Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Simplified Approach to Recovery Conditions for Low Rank Matrices   Recovering sparse vectors and low-rank matrices from noisy linear
measurements has been the focus of much recent research. Various reconstruction
algorithms have been studied, including $\ell_1$ and nuclear norm minimization
as well as $\ell_p$ minimization with $p<1$. These algorithms are known to
succeed if certain conditions on the measurement map are satisfied. Proofs of
robust recovery for matrices have so far been much more involved than in the
vector case.
  In this paper, we show how several robust classes of recovery conditions can
be extended from vectors to matrices in a simple and transparent way, leading
to the best known restricted isometry and nullspace conditions for matrix
recovery. Our results rely on the ability to "vectorize" matrices through the
use of a key singular value inequality.

25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci