77
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

The DJL Conjecture for CP Matrices over Special Inclines

&
Pages 3818-3841 | Received 25 Nov 2014, Published online: 19 May 2016

REFERENCES

  • Ahn, S. S., Kim, H. S. (2002). On r-ideals in incline algebras. Commun. Korean Math. Soc. 17(2):229–235.
  • Berman, A., Shaked-Monderer, N. (1998). Remarks on completely positive matrices. Linear and Multilinear Algebra 44:149–163.
  • Berman, A., Shaked-Monderer, N. (2003). Completely Positive Matrices. River Edge, NJ: World Scientific.
  • Butkovič, P. (2003). Max-algebra: The linear algebra of combinatorics? Linear Algebra Appl. 367:313–335.
  • Bomze, I. M., Schachinger, W., Ullrich, R. (2014). From seven to eleven: Completely positive matrices with high cp-rank. Linear Algebra and Its Applications 459:208–221.
  • Bomze, I. M., Schachinger, W., Ullrich, R. (2015). New lower bounds and asymptotics for the CP rank. SIAM J. Matrix Anal. 36:20–37.
  • Cao, Z. Q. (1983). An algebraic system generalizing the fuzzy subsets of a set. Advances in Fuzzy Sets, Possibility Theory, and Applications. New York: Plenum, pp. 71–80.
  • Cao, Z. Q., Kim, K. H., Roush, F. W. (1984). Incline Algebra and Applications. Ellis Horwood, Chichester, England, New York: Wiley.
  • Duan, J.-S., Guo, A.-P., Zhao, F.-X., Xu, L., Tang, W.-G. (2011). Standard bases of a vector space over a linearly ordered incline. Communications in Algebra 39(4): 1404–1412.
  • Drew, J. H., Johnson, C. R. (1996). The no long odd cycle theorem for completely positive matrices. In: Aldous, D. Pemantle, R. eds. Random Discrete Structures. IMA Vol. Math. Appl., Vol. 76. New York: Springer, pp. 103–115.
  • Drew, J. H., Johnson, C. R., Loewy, R. (1994). Completely positive matrices associated with M-matrices. Linear and Multilinear Algebra 37:303–310.
  • Golan, J. S. (1990). Semirings for the ring theorist. Rev. Roumaine Math. Pures Appl. 35(6):531–540.
  • Hannah, J., Laffey, T. L. (1983). Nonnegative factorization of completely positive matrices. Linear Algebra and Its Applications 55:1–9.
  • Han, S.-C., Ri, H.-R. (2013). The only regular inclines are distributive lattices. Romanian Journal of Mathematics and Computer Science 3(2):160–163.
  • Johnson, C. R., Nasserasr, S. (2010). TP2 = Bruhat. Discrete Math. 310:1627–1628.
  • Kaykobad, M. (1987). On nonnegative factorization of matrices. Linear Algebra and Its Applications 96:23–33.
  • Kim, K. H., Roush, F. W. (2004). Inclines and incline matrices: A survey. Linear Algebra and Its Applications 379:457–473.
  • Lau, C. M., Markham, T. L. (1978). Square triangular factorizations of completely positive matrices. J. Industrial Math. Soc. 28:15–24.
  • Loewy, R., Tam, B.-S. (2003). CP rank of completely positive matrices of order five. Linear Algebra and Its Applications 363:161–176.
  • Markham, T. L. (1971). Factorization of completely positive matrices. Proc. Cambridge Philos. Soc. 69:53–58.
  • Mohindru, P. (2015). The Drew-Johnson-Loewy conjecture for matrices over max-min semirings. Linear and Multilinear Algebra 63:914–926.
  • Mohindru, P., Pereira, R. Orderings on semirings and completely positive matrices. To appear in Linear and Multilinear Algebra, doi:10.1080/03081087.2015.1059405.
  • Plus, M. (1990). Linear systems in (max, +) algebra. In: Proceedings of the 29th Conference on Decision and Control, Honolulu, Dec.
  • Poplin, P. L., Hartwig, R. E. (2004). Determinantal identities over commutative semirings. Linear Algebra and Its Applications 387:99–132.
  • Shaked-Monderer, N. (2001). Minimal CP rank. The Electronic Journal of Linear Algebra 8:140–157.
  • Shaked-Monderer, N., Bomze, I. M., Jarre, F., Schachinger, W. (2013). On the CP-rank and minimal CP factorizations of a completely positive matrix. SIAM Journal of Matrix Analysis and Applications 34(2):355–368.
  • Vandiver, H. S. (1934). Note on a simple type of algebra in which the cancellation law of addition does not hold. Bull. Amer. Math. Soc. 40:914–920.
  • Zhan, X. (2008). Open problems in matrix theory. Proceedings of the 4th International Congress of Chinese Mathematicians. 1:367–382.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.