Column normalization of a random measurement matrix

Blind Measurement Selection: A Random Matrix Theory Approach

This paper considers the problem of selecting a set of k measurements from n available sensor observations. The selected measurements should minimize a certain error function assessing the error in estimating a certain m dimensional parameter vector. The exhaustive search inspecting each of the ( n k ) possible choices would require a very high computational complexity and as such is not practi...

Normalization sum rule and spontaneous breaking of U(N) invariance in random matrix ensembles.

It is shown that the two-level correlation function R(s, s′) in the invariant random matrix ensembles (RME) with soft confinement exhibits a ”ghost peak” at s ≈ −s′. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term var(n) = ηn that is typical of RME with broken U(N) symmetry. Thus we conclude that the U(N) invariance is broken spontaneously in the RM...

\random" Random Matrix Products

The Column Space and the Null Space of a Matrix

On the Number of Matrices and a Random Matrix with Prescribed Row and Column Sums and 0-1 Entries

We consider the set Σ(R, C) of all m×n matrices having 0-1 entries and prescribed row sums R = (r1, . . . , rm) and column sums C = (c1, . . . , cn). We prove an asymptotic estimate for the cardinality |Σ(R, C)| via the solution to a convex optimization problem. We show that if Σ(R, C) is sufficiently large, then a random matrix D ∈ Σ(R, C) sampled from the uniform probability measure in Σ(R, C...