Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices

An upper bound for permanents of nonnegative matrices

A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in lp is attained either for the identity matrix I or for a constant multiple of the all-1 matrix J . The conjecture is known to be true for p = 1 (I) and for p ≥ 2 (J). We prove the conjecture for a subinterval of (1, 2), and...

Perturbing non-real eigenvalues of nonnegative real matrices

An upper bound for the largest Lyapunov exponent of a Markovian product of nonnegative matrices

We derive an upper bound for the largest Lyapunov exponent of a Markovian product of nonnegative matrices using Markovian type counting arguments. The bound is expressed as the maximum of a nonlinear concave function over a finite-dimensional convex polytope of probability distributions. ∗Research supported by ONR MURI N00014-1-0637, DARPA grant No. N66001-00-C8062, and by NSF contract ECS 0123...

An Upper Bound to the Marginal PDF of the Ordered Eigenvalues of Wishart Matrices

Diversity analysis of a number of Multiple-Input Multiple-Output (MIMO) applications requires the calculation of the expectation of a function whose variables are the ordered multiple eigenvalues of a Wishart matrix. In order to carry out this calculation, we need the marginal pdf of an arbitrary subset of the ordered eigenvalues. In this letter, we derive an upper bound to the marginal pdf of ...

Hoffman Polynomials of Nonnegative Irreducible Matrices and Strongly Connected Digraphs

For a nonnegative n× n matrix A, we find that there is a polynomial f(x) ∈ R[x] such that f(A) is a positive matrix of rank one if and only if A is irreducible. Furthermore, we show that the lowest degree such polynomial f(x) with tr f(A) = n is unique. Thus, generalizing the well-known definition of the Hoffman polynomial of a strongly connected regular digraph, for any irreducible nonnegative...