Solvability of Inverse Eigenvalue Problem for Dense Singular Symmetric Matrices

摘要

Given a list of real numbers ∧={λ1,…, λn}, we determine the conditions under which ∧will form the spectrum of a dense n × n singular symmetric matrix. Based on a solvability lemma, an algorithm to compute the elements of the matrix is derived for a given list ∧ and dependency parameters. Explicit computations are performed for n≤5 and r≤4 to illustrate the result.