  We propose a new pivotal method for estimating high-dimensional matrices.
Assume that we observe a small set of entries or linear combinations of entries
of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for
estimating $A\_0$ which does not rely on the knowledge or an estimation of the
standard deviation of the noise $\sigma$. Our estimator achieves, up to a
logarithmic factor, optimal rates of convergence under the Frobenius risk and,
thus, has the same prediction performance as previously proposed estimators
which rely on the knowledge of $\sigma$. Our method is based on the solution of
a convex optimization problem which makes it computationally attractive.
