Diagonal entries of the combined matrix of sign regular matrices of order three
DOI:
https://doi.org/10.22199/issn.0717-6279-2021-01-0016Keywords:
Sign regular matrices, Combined matrices , Hadamard productAbstract
The study of the diagonal entries of the combined matrix of a nonsingular matrix A has been considered by different authors for the classes of M—matrices, positive definite matrices and totally positive (negative) matrices. This problem appears to be difficult as the results have been done only for matrices of order three. In this work, we continue to give the characterization of the diagonal entries of the combined matrix of the remainder sign regular matrices. Thus, the problem is closed for all possible sign regular matrices of order three.
References
P. Alonso and M. L. Serrano, “Combined matrices of almost strictly sign regular matrices”, Journal of computational and applied mathematics, vol. 354, pp. 144-151, Jul. 2019, doi: 10.1016/j.cam.2018.09.029
E. Bristol, “On a new measure of interaction for multivariable process control”, IEEE transactions on automatic control, vol. 11, no. 1, pp. 133–134, Jan. 1966, doi: 10.1109/TAC.1966.1098266
R. Bru, M. Gassó, I. Giménez, and M. Santana, “Combined matrices of sign regular matrices”, Linear algebra applications, vol. 498, pp. 88-98, Jun. 2016. doi: 10.1016/j.laa.2014.12.010
R. Bru, M. Gassó, I. Giménez, and M. Santana, “Diagonal entries of the combined matrix of a totally negative matrix”, Linear and multilinear algebra, vol. 65, no. 10, pp 1971-1984, 2017, doi: 10.1080/03081087.2016.1261079
M. Fiedler, “Relations between the diagonal entries of an M-matrix and of its inverse”, Matematicko-fyzikálny časopis, vol. 12, no. 2, pp. 123-128, 1962. [On line]. Available: https://bit.ly/2XHudbq
M. Fiedler, “Relations between the diagonal entries of two mutually inverse positive definite matrices”, Czechoslovak mathematics journal, vol. 14, no.1, pp. 39-51, 1964, doi: 10.21136/cmj.1964.100600
M. Fiedler and T. L. Markham, “Combined matrices in special classes of matrices”, Linear algebra applications, vol. 435, no. 8, pp. 1945-1955, Oct. 2011, doi: 10.1016/j.laa.2011.03.054
R. A. Horn and C. R. Johnson, Topics in matrix analysis. Cambridge: Cambridge University Press, 1991, doi: 10.1017/CBO9780511840371
J. M. Peña, “On nonsingular sign regular matrices”, Linear algebra and applications, vol. 359, no. 1-3, pp. 91-100, Jan. 2003, doi: 10.1016/S0024-3795(02)00437-8
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Copyright (c) 2021 Maria T. Gassó, Iv´an Gil, Isabel Giménez, M´aximo Santana, Elaine Segura
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