The Eigenvalues of EDMs

Abdo Y. Alfakih
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Abdo Y. Alfakih: University of Windsor, Department of Mathematics and Statistics

Chapter Chapter 6 in Euclidean Distance Matrices and Their Applications in Rigidity Theory, 2018, pp 121-143 from Springer

Abstract: 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 = T ( D ) = − J D J ∕ 2 $$B =\mathcal{ T}(D) = -JDJ/2$$ . 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-97846-8_6

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DOI: 10.1007/978-3-319-97846-8_6

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