On a spectral property of doubly stochastic matrices and its application to their inverse eigenvalue problem
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For the transformed doubly stochastic matrix, all eigenvalues are real and smaller than or equal to 1, with one eigenvalue exactly equal to 1.
“For this transformed matrix, all eigenvalues are real and smaller than or equal to 1, with one eigenvalue exactly equal to 1.”
From Chance constrained day-ahead robust flexibility needs assessment for low voltage distribution network (2022) · cites this paper as [41]
The Introduction (page unavailable in our copy) states that a doubly stochastic matrix has an eigenvalue of 1 and that every eigenvalue has modulus at most 1. It does not say all eigenvalues are real; Theorem 3.3 in §3, Applications (page unavailable), gives a doubly stochastic matrix with potentially nonreal eigenvalues. The cited paper therefore supports the eigenvalue bound and the eigenvalue at 1, but not the claim that all eigenvalues of the transformed matrix are real. (LLM, conf=0.88)
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Research works printed but not linked: 7
- R.B. Bapat, T.E.S. Raghavan, Non-negative Matrices and Applications, Cambridge University, Cambridge, 1997.
- I. Bengtsson, The importance of being unistochastic, 2003. arXiv:quant-ph/0403088 v1. · arXiv
- I. Bengtsson, Å. Ericsson, M. Kuś, W. Tadej, K. Życzkowski, Birkoff's polytope and unistochastic matrices: N = 3 and N = 4, 2004. arXiv:math.CO/0402325 v2. · arXiv
- R. Bhatia, Matrix Analysis, Springer-Verlag, New York, 1997.
- M.T. Chu, G.H. Golub, Inverse Eigenvalue Problems: Theory, Algorithms and Applications, Oxford University Press, 2005.
- H. Minc, Non-negative Matrices, Berlin Press, New York, 1988.
- E. Seneta, Non-negative Matrices and Markov Chains, second ed., Springer, New York, 1981.
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Hashmi, M. U., Koirala, A., Ergun, H., & Van Hertem, D. (2022) · arXiv · doi:10.48550/arxiv.2207.10234 · Cited by 1 · see citing works
- Authors
- Mourad, B.
- Affiliations
- Lebanese University (LB)
- Corresponding author
- Mourad, Bassam
- ORCID
- Mourad, Bassam
- Venue
- Linear Algebra and its Applications
- Publisher
- Elsevier BV
- Published
- 2012-05
- Volume
- 436
- Issue
- 9
- Pages
- 3400-3412
- ISSN
- 0024-3795 (ISSN-L)
- OpenAlex
- W2019274474
- Cited by
- 23
- References
- 0
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 5 · 2022: 1 · 2020: 2 · 2019: 2 · 2018: 1 · 2017: 1 · 2016: 1 · 2014: 2 · 2013: 4 · 2012: 1
- FWCI
- 2.12
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Linear Algebra and its Applications (publishedVersion)
- Funders
- Université Libanaise
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Geometry and Topology › Graph theory and applications
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- doubly stochastic matrices, spectral properties, inverse eigenvalue problem, sufficient conditions, matrix eigenvalues
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