Open AccessBlock Representation and Spectral Properties of Constant Sum Matrices
Author(s) -
Sheila Hill,
Matthew C. Lettington,
Karl Michael Schmidt
Publication year - 2018
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/1081-3810.3530
Subject(s) - mathematics , eigenvalues and eigenvectors , constant (computer programming) , equivalence (formal languages) , representation (politics) , block (permutation group theory) , pure mathematics , algebra over a field , combinatorics , computer science , physics , quantum mechanics , politics , political science , law , programming language
An equivalent representation of constant sum matrices in terms of block-structured matrices is given in this paper. This provides an easy way of constructing all constant sum matrices, including those with further symmetry properties. The block representation gives a convenient description of the dihedral equivalence of such matrices. It is also shown how it can be used to study their spectral properties, giving explicit formulae for eigenvalues and eigenvectors in special situations, as well as for quasi-inverses when these exist.