Ela Symmetric Nonnegative
نویسنده
چکیده
A perturbation result, due to R. Rado and presented by H. Perfect in 1955, shows how to modify r eigenvalues of a matrix of order n, r ≤ n, via a perturbation of rank r, without changing any of the n − r remaining eigenvalues. This result extended a previous one, due to Brauer, on perturbations of rank r = 1. Both results have been exploited in connection with the nonnegative inverse eigenvalue problem. In this paper a symmetric version of Rado’s extension is given, which allows us to obtain a new, more general, sufficient condition for the existence of symmetric nonnegative matrices with prescribed spectrum.
منابع مشابه
Ela on Nonnegative
We consider partitioned lists of real numbers Λ = {λ1, λ2, . . . , λn}, and give efficient and constructive sufficient conditions for the existence of nonnegative and symmetric nonnegative matrices with spectrum Λ. Our results extend the ones given in [R.L. Soto and O. Rojo. Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem. Linear Algebra Appl., 416:844– 856, 2006....
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