References
- [1] Armandnejad, A., Akbarzadeh, F., and Mohammadi, Z.; Row and column-majorization on Mn,m, Linear Algebra and its applications, 437(2012), 1025-1032.
- [2] Birkhoff, G.; Tresobservacionessobre el algebra lineal, Univ. Nac. Tucumán Rev. Se. A 5 (1946), 147-151.
- [3] Bhuiyan, M. A. M.; Predicting Stochastic Volatility For Extreme Fluctuations In High Frequency Time Series. Open Access Theses & Dissertations (2020), 2934.
- [4] Cheng, Y., Carson, T. and Elgindi, M. B. M.; A Note on the Proof of the Perron-Frobenius Theorem, Applied Mathematics 3(11) (2012).
- [5] Chruściński, D.; Positive maps, doubly stochastic matrices and new family of spectral conditions, Journal of Physics: Conference Series, IOP Publishing, 213(1) (2010), 012003.
- [6] Chruściński, D., and Kossakowski. A.; Spectral conditions for positive maps and entanglement witnesses. Journal of Physics: Conference Series. IOP Publishing, 284(1) (2011) 012017.
- [7] Das, H. K.; Affine Integral Quantization on a Coadjoint Orbit of the Poincaré Group in (1+1)-space-time Dimensions and Applications. Masters thesis, Concordia University (2015).
- [8] Dahl, G.; Matrix majorization, Linear Algebra and Its Applications 288(1999), 53-73.
- [9] Dmitriev, N. and Dynkin, E.; On characteristic roots of stochastic matrices”, Izv. Akad. Nauk SSSR Ser. Mat., 10(2) (1946), 167–184.
- [10] Gagniuc, P. A.; Markov Chains: From Theory to Implementation and Experimentation, John Wiley & Sons (2017).
- [11] Ito, H.; A new statement about the theorem determining the region of eigenvalues of stochastic matrices, Linear algebra and its applications, 267 (1997), 241-246.
- [12] Jamiołkowski, A. (1972). Linear transformations which preserve trace and positive semidefiniteness of operators. Reports on Mathematical Physics, 3(4), 275-278.
- [13] Karpelevič, F. I.; On characteristic roots of matrices with nonnegative coefficients, Uspehi Matem. Nauk (NS) 4.5 (33) (1949), 177-178.
- [14] Kendall D. G., G. K. Batchelor, N. H. Bingham, W. K. Hayman, J. M. E. Hyland, G. G. Lorentz, H. K. Moffatt, W. Parry, A. A. Razborov, C. A. Robinson, P. Whittle.: Andrei Nikolaevich Kolmogorov (1903–1987), Bulletin of the London Mathematical Society, 22(1) (1990), 31-100.
- [15] Kra, I., and Simanca, S. R.; On circulant matrices, Notices of the AMS 59(3) (2012), 368-377.
- [16] Kraus, K., Böhm, A., Dollard, J. D., and Wootters W. H.; States, effects and operations: fundamental notions of quantum theory, Springer (1983).
- [17] Levick, J.; An Uncertainty Principle For Completely Positive Maps. Preprint arXiv:1611.06352 (2016).
- [18] Levick, J.; New Methods for the Perfect-Mirsky Conjecture and Private Quantum Channels. Ph.D. thesis, University of Guelph (2015).
- [19] Levick, J., Pereira, R. and Kribs, D. W.; The four-dimensional Perfect-Mirsky conjecture, Proceedings of the American Mathematical Society 143 (5) (2015), 1951–1956.
- [20] Marshall, A. W., Olkin, I and Arnold, B. C.; Inequalities: theory of majorization and its applications, New York (1979).
- [21] Mashreghi, J. and Rivard, R.; On a conjecture about the eigenvalues of doubly stochastic matrices, Linear and Multilinear Algebra 55(5) (2007), 491-498.
- [22] Mehlum, M. S.; Doubly Stochastic Matrices and the Assignment Problem, MS thesis, (2012).
- [23] Perfect, H., and Mirsky. L., Seffield; Spectral properties of doubly-stochastic matrices, Monatshefte für Mathematik 69 (1965): 35-57.
- [24] Poon, Y. T.; Quantum operations, Summer School on Quantum Information Science Taiyuan University of Technology, Taiyuan, Shanxi, China, July 18 - 22 (2011).
- [25] Prashanth B., K Nagendra Naik, KR Rajanna. A remark on eigen values of signed graph, Journal of Applied Mathematics, Statistics and Informatics, 15(1) (2019): 33-42.
- [26] Romanovsky, V; Recherchessur les chaines de Markoff, Acta mathematica 66(1) (1936): 147 - 251.
- [27] Samad, S.G. and W. N. Polyzou; Euclidean formulation of relativistic quantum mechanics of N particles, Physical Review C 103 (2021): 025203-22.