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The Eigenvalues of EDMs

  • Abdo Y. Alfakih
Chapter

Abstract

The focus of this chapter is on the eigenvalues of EDMs. In the first part, we present a characterization of the column space of an EDM D. This characterization is then used to express the eigenvalues of D in terms of the eigenvalues of its Gram matrix \(B =\mathcal{ T}(D) = -JDJ/2\). In case of regular and nonspherical centrally symmetric EDMs, the same result can also be obtained by using the notion of equitable partition. In the second part, we discuss some other topics related to eigenvalues such as: a method for constructing nonisomorphic cospectral EDMs; the connection between EDMs, graphs, and combinatorial designs; EDMs with exactly two or three distinct eigenvalues and the EDM inverse eigenvalue problem.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Abdo Y. Alfakih
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of WindsorWindsorCanada

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