ARTICLE | doi:10.20944/preprints202008.0272.v1
Subject: Computer Science And Mathematics, Computational Mathematics Keywords: Bohemian; Toeplitz matrix; Hessenberg matrix; tridiagonal matrix; pentadiagonal matrix
Online: 12 August 2020 (06:00:31 CEST)
In this paper, we deduce explicit formulas to evaluate the determinants of nonsymmetrical structure Toeplitz Bohemians by two determinants of specific Hessenberg Toeplitz matrices, which are linear combinations in terms of determinants of specific Hessenberg Toeplitz matrices. We get some new results very di¤erent from [Massimiliano Fasi, Gian Maria Negri Porzio, Determinants of normalized upper Hessenberg matrices, Electronic Journal of Linear Algebra, Volume 36, pp. 352-366, June 2020].
ARTICLE | doi:10.20944/preprints201903.0010.v1
Subject: Computer Science And Mathematics, Geometry And Topology Keywords: Toeplitz quantization, decreasing rearrangement, majorization, spectral measure, measure preserving transformation, Hermitian matrices
Online: 1 March 2019 (12:25:47 CET)
In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.