Yang, Shang-Jun; Xu, Chang-Qing Row stochastic inverse eigenvalue problem. (English) Zbl 1269.15008 J. Inequal. Appl. 2011, Paper No. 24, 5 p. (2011). Summary: We give sufficient conditions or realizability criteria for the existence of a row stochastic matrix with a given spectrum \(\Lambda = \{\lambda_1, \dots, \lambda_n\} = \Lambda_1 \cup \ldots \cup \Lambda_m \cup \Lambda_{m+1}\), \(m > 0\); where \(\Lambda_k=\{\lambda_{k1}, \lambda_{k2},\dots, \lambda_{kp_k}\}= \{\lambda_{k1}, \omega_{k}e^{2\pi i/p_k}, \omega_ke^{4\pi i/p_k},\dots, \omega_ke^{2(p_k-1)\pi i/p_k}\}\) (\(p_k\) is an integer greater than 1), \(\lambda_{k1}=\lambda_k > 0\), \(1 = \lambda_1 \geq \omega_k > 0\), \(k =1, \dots, m\); \(\Lambda_{m+1} = \{\lambda_m+1\}\), \(\omega_ {m+1} \equiv \lambda_1 + \dots + \lambda_n \leq \lambda_1\), \(\omega_k \geq \lambda_k\), \(\omega_1 \geq \lambda_k\), \(k= 2, \ldots, m+1\). In the case when \(p_1, \dots, p_m \) are all equal to \(2\), \(\Lambda\) becomes a list of \(2m + 1\) real numbers for any positive integer \(m\), and our result gives sufficient conditions for a list of \(2m + 1\) real numbers to be realizable by a row stochastic matrix. Cited in 2 Documents MSC: 15A18 Eigenvalues, singular values, and eigenvectors 15A29 Inverse problems in linear algebra 15B51 Stochastic matrices Keywords:row stochastic matrices; inverse eigenvalue problem; row stochastic inverse eigenvalue problem PDFBibTeX XMLCite \textit{S.-J. Yang} and \textit{C.-Q. Xu}, J. Inequal. Appl. 2011, Paper No. 24, 5 p. (2011; Zbl 1269.15008) Full Text: DOI References: [1] doi:10.1016/j.laa.2005.12.026 · Zbl 1097.15014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.