Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Some results on the q-numerical range of matrix polynomials

Document Type : Original Paper

Authors
Department of mathematics, Payame noor university, Tehran, Iran
Abstract
The set of q-numerical range of order a as one of the generalizations of the numerical range of square matrices, is introduced in this paper. Some of its algebraic and geometrical properties, such as the number of connected components and its symmetries, are investigated, and considering the obtained relations, inequalities regarding the q-numerical radius and the inner q-numerical radius are obtained.
Keywords
Subjects

[1] Aghamollaei, Gh., Avizeh, N. and Jahanshahi, Y., 2013. Generalized numerical ranges of matrix polynomials. Bull. Iranian Math. Soc., 39(5), pp. 789-803. DOI:not available
[2] Chein, M., Nakazato, H. and Psarrakos, P., 2006. The q-numerical range and the DavisWielandt shell of reducible 3 × 3 matrices. Linear Multilinear Algebra, 54(2), pp. 79-112. DOI:
10.1080/00036810500148994
[3] Horn, R. A., and Johnson, C. R., 2012. Matrix analysis . Cambridge University Press, 2nd edition, .
[4] Li, C. K., Mehta, P. P., and Rodman, L., 1994. A generalized numerical range: the range
of a constrained sesquilinear form. Linear Multilinear Algebra, 37(1-3), pp. 25-49. DOI:
10.1080/03081089408818311
[5] Marcus, M., and Andersen, P., 1977. Constrained extrema of bilinear functionals. Monatsh Math., 84,
pp. 219-235. DOI: 10.1007/BF01538033
[6] Psarrakos, P. J., 2001, The q−numerical range of matrix polynomials, II, Bull. Greek Math. Soc., 45,
pp. 3-15. DOI: not available
[7] Psarrakos, P. J., and Vlamos, P. M., 1998. The q−numerical range of matrix polynomials. Linear
Multilinear Algebra, 47(1), pp. 1-9. DOI: 10.1080/03081080008818627
[8] Rezagholi, Sh. and Yasini, R., 2024. Index rank−k numerical range of matrices. J. Mahani Math.
Res., 13(1), pp. 525-534. DOI: 10.22103/jmmr.2023.21566.1445
[9] Safarzadeh, M. and Salemi, A., 2018. DGMRES and index numerical range of matrices. J. Comput.
Appl. Math., 335, pp. 349-360. DOI: 10.1016/j.cam.2017.12.009

  • Receive Date 06 May 2025
  • Revise Date 19 July 2025
  • Accept Date 29 September 2025