Acknowledgement
Supported by : National Research Foundation of Korea
References
- L. B. Beasley, A. E. Guterman, and Y. Shitov, The arctic rank of a Boolean matrix, J. Algebra 433 (2015), 168-182. https://doi.org/10.1016/j.jalgebra.2015.03.005
- L. B. Beasley and N. J. Pullman, Boolean-rank-preserving operators and Boolean-rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77. https://doi.org/10.1016/0024-3795(84)90158-7
- L. B. Beasley and N. J. Pullman, Term-rank, permanent, and rook-polynomial preservers, Linear Algebra Appl. 90 (1987), 33-46. https://doi.org/10.1016/0024-3795(87)90302-8
- L. B. Beasley and S.-Z. Song, Primitive symmetric matrices and their preservers, Linear Multilinear Algebra 65 (2017), no. 1, 129-139. https://doi.org/10.1080/03081087.2016.1175414
- L. B. Beasley and S.-Z. Song, Symmetric arctic ranks of nonnegative matrices and their linear preservers, Linear Multilinear Algebra 65 (2017), no. 10, 2000-2010. https://doi.org/10.1080/03081087.2017.1282931
- K. H. Kim and F. W. Roush, Kapranov rank vs. tropical rank, Proc. Amer. Math. Soc. 134 (2006), no. 9, 2487-2494. https://doi.org/10.1090/S0002-9939-06-08426-7
- T. Markham, Factorizations of completely positive matrices, Proc. Cambridge Philos. Soc. 69 (1971), 53-58. https://doi.org/10.1017/s0305004100046405
- S. Pierce, Algebraic sets, polynomials, and other functions, Linear and Multilinear Algebra 33 (1992), no. 1-2, 31-52. https://doi.org/10.1080/03081089208818180
- S. Z. Song, L. B. Beasley, P. Mohindru, and R. Pereira, Preservers of completely positive matrix rank, Linear Multilinear Algebra 64 (2016), no. 7, 1258-1265. https://doi.org/10.1080/03081087.2015.1082960
- S.-Z. Song, K.-T. Kang, and L. B. Beasley, Linear operators that preserve perimeters of matrices over semirings, J. Korean Math. Soc. 46 (2009), no. 1, 113-123. https://doi.org/10.4134/JKMS.2009.46.1.113