  The joint sparse recovery problem is a generalization of the single
measurement vector problem which is widely studied in Compressed Sensing and it
aims to recovery a set of jointly sparse vectors. i.e. have nonzero entries
concentrated at common location. Meanwhile l_p-minimization subject to matrices
is widely used in a large number of algorithms designed for this problem.
Therefore the main contribution in this paper is two theoretical results about
this technique. The first one is to prove that in every multiple systems of
linear equation, there exists a constant p* such that the original unique
sparse solution also can be recovered from a minimization in l_p quasi-norm
subject to matrices whenever 0< p<p*. The other one is to show an analysis
expression of such p*. Finally, we display the results of one example to
confirm the validity of our conclusions.
