Pierre Youssef

activity

20122026

most citedThe dimension-free structure of nonhomogeneous random matrices

48 citations · 137 across the 28 of their papers we have counts for

collaborators

Showing math.FAShow all

5 papers · 1 filter

math.FA2016★ 16 cited

Approximating matrices and convex bodies through Kadison-Singer

Omer Friedland, Pierre Youssef

We show that any $n \times m$ matrix $A$ can be approximated in operator norm by a submatrix with a number of columns of order the stable rank of $A$ . This improves on existing resu…

math.FA2016

Restricted invertibility revisited

Assaf Naor, Pierre Youssef

Suppose that $m, n \in N$ and that $A : R^{m} \to R^{n}$ is a linear operator. It is shown here that if $k, r \in N$ satisfy $k < r \leq rank (A)$ …

math.FA2014

Extracting a basis with fixed block inside a matrix

Pierre Youssef

Given $U$ an $n \times m$ matrix of rank $n$ and $V$ block of columns inside $U$ , we consider the problem of extracting a block of columns of rank $n$ which minimize the Hilbert-Sch…

math.FA2012★ 7 cited

A note on column subset selection

Pierre Youssef

Given a matrix U, using a deterministic method, we extract a "large" submatrix of U'(whose columns are obtained by normalizing those of U) and estimate its smallest and largest sin…

math.FA2012★ 24 cited

Restricted Invertibility and the Banach-Mazur distance to the cube

Pierre Youssef

We prove a normalized version of the restricted invertibility principle obtained by Spielman-Srivastava. Applying this result, we get a new proof of the proportional Dvoretzky-Roge…