Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	Complete spectral theory for matrices over a field whose graph is a star
Publication Date:	2019-05-23
Authors:	- Charles R. Johnson - António Leal Duarte
Abstract:	For matrices over a field 𝔽, whose graph is a star, any characteristic polynomial may occur if \|𝔽\| is large enough. Depending upon the diagonal entries, some linear factors will have to occur, but given this, the characteristic polynomial is still arbitrary. For smaller fields, a characterization of achievable polynomials is given. The geometrically multiple eigenvalues are easily identified, and, given this, the Jordan structure is completely determined. It turns out that no eigenvalue may enjoy more that one block of size greater than one, a restriction not present in all trees.
Institution:	DMUC 19-17
Online version:	http://www.mat.uc.pt...prints/eng_2019.html
Download:	Not available