Construction of 4 x 4 symmetric stochastic matrices with given spectra

Author:

Jung Jaewon1,Kim Donggyun1

Affiliation:

1. Department of Mathematics, Korea University , Seongbuk-gu , Seoul, 02841 , Korea

Abstract

Abstract The symmetric stochastic inverse eigenvalue problem (SSIEP) asks which lists of real numbers occur as the spectra of symmetric stochastic matrices. When the cardinality of a list is 4, Kaddoura and Mourad provided a sufficient condition for SSIEP by a mapping and convexity technique. They also conjectured that the sufficient condition is the necessary condition. This study presents the same sufficient condition for SSIEP, but we do it in terms of the list elements. In this way, we provide a different but more straightforward construction of symmetric stochastic matrices for SSIEP compared to those of Kaddoura and Mourad.

Publisher

Walter de Gruyter GmbH

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