Geodesic
A note on classes of structured matrices with elliptical type numerical range
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1015-1023
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We identify new classes of structured matrices whose numerical range is of the elliptical type, that is, an elliptical disk or the convex hull of elliptical disks.
We identify new classes of structured matrices whose numerical range is of the elliptical type, that is, an elliptical disk or the convex hull of elliptical disks.
DOI : 10.21136/CMJ.2021.0174-20
Classification : 15A21, 15A60
Keywords: tridiagonal matrix; antitridiagonal matrix; elliptical disk; numerical range 
@article{10_21136_CMJ_2021_0174_20,
     author = {Bebiano, Nat\'alia and Furtado, Susana},
     title = {A note on classes of structured matrices with elliptical type numerical range},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1015--1023},
     year = {2021},
     volume = {71},
     number = {4},
     doi = {10.21136/CMJ.2021.0174-20},
     mrnumber = {4339107},
     zbl = {07442470},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0174-20/}
}
TY  - JOUR
AU  - Bebiano, Natália
AU  - Furtado, Susana
TI  - A note on classes of structured matrices with elliptical type numerical range
JO  - Czechoslovak Mathematical Journal
PY  - 2021
SP  - 1015
EP  - 1023
VL  - 71
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0174-20/
DO  - 10.21136/CMJ.2021.0174-20
LA  - en
ID  - 10_21136_CMJ_2021_0174_20
ER  - 
%0 Journal Article
%A Bebiano, Natália
%A Furtado, Susana
%T A note on classes of structured matrices with elliptical type numerical range
%J Czechoslovak Mathematical Journal
%D 2021
%P 1015-1023
%V 71
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0174-20/
%R 10.21136/CMJ.2021.0174-20
%G en
%F 10_21136_CMJ_2021_0174_20
Bebiano, Natália; Furtado, Susana. A note on classes of structured matrices with elliptical type numerical range. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1015-1023. doi: 10.21136/CMJ.2021.0174-20

[1] Bebiano, N., Providência, J. da, Nata, A.: The numerical range of banded biperiodic Toeplitz operators. J. Math. Anal. Appl. 398 (2013), 189-197. | DOI | MR | JFM

[2] Bebiano, N., Furtado, S.: Remarks on anti-tridiagonal matrices. Appl. Math. Comput. 373 (2020), Article ID 125008, 10 pages. | DOI | MR | JFM

[3] Bebiano, N., Spitkovsky, I. M.: Numerical ranges of Toeplitz operators with matrix symbols. Linear Algebra Appl. 436 (2012), 1721-1726. | DOI | MR | JFM

[4] Brown, E. S., Spitkovsky, I. M.: On matrices with elliptical numerical ranges. Linear Multilinear Algebra 52 (2004), 177-193. | DOI | MR | JFM

[5] Chien, M.-T.: On the numerical range of tridiagonal operators. Linear Algebra Appl. 246 (1996), 203-214. | DOI | MR | JFM

[6] Chien, M.-T., Nakazato, H.: The numerical range of a tridiagonal operator. J. Math. Anal. Appl. 373 (2011), 297-304. | DOI | MR | JFM

[7] Chien, R. T., Spitkovsky, I. M.: On the numerical ranges of some tridiagonal matrices. Linear Algebra Appl. 470 (2015), 228-240. | DOI | MR | JFM

[8] Chien, M.-T., Yeh, L., Yeh, Y.-T., Lin, F.-Z.: On geometric properties of the numerical range. Linear Algebra Appl. 274 (1998), 389-410. | DOI | MR | JFM

[9] Eiermann, M.: Field of values and iterative methods. Linear Algebra Appl. 180 (1993), 167-197. | DOI | MR | JFM

[10] Geryba, T., Spitkovsky, I. M.: On the numerical range of some block matrices with scalar diagonal blocks. (to appear) in Linear and Multilinear Algebra. | DOI

[11] Gustafson, K. E., Rao, D. K. M.: Numerical Range: The Field of Values of Linear Operators and Matrices. Universitext. Springer, New York (1997). | DOI | MR | JFM

[12] Horn, R. A., Johnson, C. R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991). | DOI | MR | JFM

[13] Kippenhahn, R.: Über den Wertevorrat einer Matrix. Math. Nachr. 6 (1951), 193-228 German. | DOI | MR | JFM

[14] Klein, E. M.: The numerical range of a Toeplitz operator. Proc. Am. Math. Soc. 35 (1972), 101-103. | DOI | MR | JFM

[15] Marcus, M., Pesce, C.: Computer generated numerical ranges and some resulting theorems. Linear and Multilinear Algebra 20 (1987), 121-157. | DOI | MR | JFM

[16] Rault, P. X., Sendova, T., Spitkovsky, I. M.: 3-by-3 matrices with elliptical numerical range revisited. Electron. J. Linear Algebra 26 (2013), 158-167. | DOI | MR | JFM

Cité par Sources :