## Upper Hessenberg and Toeplitz Bohemian matrix sequences: a note on their asymptotical eigenvalues and singular values

Manuel Bogoya, Stefano Serra-Capizzano, and Ken Trotti

### Abstract

In previous works, Bohemian matrices have attracted the attention of several researchers for their rich combinatorial structure, and they have been studied intensively from several points of view, including height, determinants, characteristic polynomials, normality, and stability. Here we consider a selected number of examples of upper Hessenberg and Toeplitz Bohemian matrix sequences whose entries belong to the population $P=\{0,\pm 1\}$, and we propose a connection with the spectral theory of Toeplitz matrix sequences and Generalized Locally Toeplitz (GLT) matrix sequences in order to give results on the localization and asymptotical distribution of their spectra and singular values. Numerical experiments that support the mathematical study are reported. A conclusion section ends the note in order to illustrate the applicability of the proposed tools to more general cases.

Full Text (PDF) [2.3 MB], BibTeX

### Key words

matrix (Bohemian, (upper) Hessenberg, Toeplitz), matrix sequence (Toeplitz, GLT), eigenvalue, singular value, spectral and singular value symbol/distribution

### AMS subject classifications

15B05, 15B36, 15A18, 11C20, 65F08, 65F15

### Links to the cited ETNA articles

 [1] Vol. 53 (2020), pp. 28-112 Giovanni Barbarino, Carlo Garoni, and Stefano Serra-Capizzano: Block generalized locally Toeplitz sequences: theory and applications in the unidimensional case

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