An inverse problem for symmetric doubly stochastic matrices

Details An inverse problem for symmetric doubly stochastic matrices An inverse problem for symmetric doubly stochastic matrices

Aug 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003invpr..19..821m&link_type=abstract

Inverse Problems, Volume 19, Issue 4, pp. 821-831 (2003).

Computer Science

Scientific paper

In this paper, we study the inverse eigenvalue problem for n × n symmetric doubly stochastic matrices. The spectra of all indecomposable imprimitive symmetric doubly stochastic matrices are characterized. Then we obtain new sufficient conditions for a real n-tuple to be the spectrum of an n × n symmetric doubly stochastic matrix of zero trace. Also, we prove that the set where the decreasingly ordered spectra of all n × n symmetric doubly stochastic matrices lie is not convex. As a consequence, we prove that the set where the decreasingly ordered spectra of all n × n non-negative matrices lie is not convex.

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