Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue

Abstract

Let A = [aij] be a real symmetric matrix. If f : (0, ∞) → [0, ∞) is a Bernstein function, a sufficient condition for the matrix [f (aij)] to have only one positive eigenvalue is presented. By using this result, new results for a symmetric matrix with exactly one positive eigenvalue, e.g., properties of its Hadamard powers, are derived.

Keywords

• bernstein function
• hadamard power
• hadamard inverse
• distance matrix
• infinitely divisible matrix
• conditionally negative semidefinite matrix
• 15b48
• 15b57
• 15a18
• 26a48