References
Dmitriev, N. andDynkin, E.,On the characteristic numbers of a stochastic matrix. Dokl. Adad. Nauk SSSR49 (1945), 159–162.
Johnson, C. R.,Gersgorin sets and the field of values. J. Math. Anal. Appl.45 (1974), 416–419.
Johnson, C. R.,Functional characterizations of the field of values and the convex hull of the spectrum. Proc. Amer. Math. Soc61 (1976), 201–204.
Johnson, C. R. andKellogg, R. B.,An inequality for doubly stochastic matrices. J. Res. Nat. Bur. Standards80B (1976), 433–436.
Karpelevich, F.,On the eigenvalues of a matrix with nonnegative elements. Izv. Akad. Nauk SSR Ser. Mat.15 (1951), 361–383. (Russian).
Kellogg, R. B.,On complex eigenvalues of M and P matrices. Numer. Math.19 (1972), 170–175.
Kellogg, R. B. andStephens, A.,Complex eigenvalues of a nonnegative matrix with a specified graph. Linear Algebra and Appl. (to appear).
Ryser, H.,Combinatorial Mathematics. Carus Monograph No. 14, Wiley and Sons, 1963.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Johnson, C.R. An inclusion region for the field of values of a doubly stochastic matrix based on its graph. Aequat. Math. 17, 305–310 (1978). https://doi.org/10.1007/BF01818568
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01818568