TY - JOUR
T1 - Conjectures about determining the regions of eigenvalues of stochastic and doubly stochastic matrices
AU - Kim, Bara
AU - Kim, Jeongsim
N1 - Funding Information:
We are grateful to the reviewer for their valuable comments. B. Kim's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIT ) (No. 2020R1A2B5B01001864 ). J. Kim's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIT ) (No. 2020R1F1A1A01065568 ).
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2022/3/15
Y1 - 2022/3/15
N2 - Let the regions Θn and ωn be the subsets of the complex planes that consist of all eigenvalues of all n×n stochastic and doubly stochastic matrices, respectively. Also, let Πn denote the convex hull of the nth roots of unity. Levick, Pereira and Kribs (2015) [10] made the following conjectures on the relations between Θn, ωn and Πn: ωn=Θn−1∪Πn and Θn−1⊂ωn. These two conjectures are known to be true for n=2,3,4. In this paper, we will show that these two conjectures are not true for n≥5.
AB - Let the regions Θn and ωn be the subsets of the complex planes that consist of all eigenvalues of all n×n stochastic and doubly stochastic matrices, respectively. Also, let Πn denote the convex hull of the nth roots of unity. Levick, Pereira and Kribs (2015) [10] made the following conjectures on the relations between Θn, ωn and Πn: ωn=Θn−1∪Πn and Θn−1⊂ωn. These two conjectures are known to be true for n=2,3,4. In this paper, we will show that these two conjectures are not true for n≥5.
KW - Doubly stochastic matrices
KW - Eigenvalues
KW - Stochastic matrices
UR - http://www.scopus.com/inward/record.url?scp=85121438620&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2021.12.011
DO - 10.1016/j.laa.2021.12.011
M3 - Article
AN - SCOPUS:85121438620
SN - 0024-3795
VL - 637
SP - 157
EP - 174
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -