Abstract
The geometric properties of EDMs are inherited from those of PSD matrices. Let \(\mathcal{D}^{n}\) denote the set of EDMs of order n. This chapter focuses on the geometry of \(\mathcal{D}^{n}\). In particular, we study the facial structure of \(\mathcal{D}^{n}\) and its polar, and we highlight the similarities between \(\mathcal{D}^{n}\) and the positive semidefinite cone \(\mathcal{S}_{+}^{n}\).
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- 1.
This set will be discussed in great detail in Chap. 8, where the rationale for this notion will become clear.
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Alfakih, A.Y. (2018). The Geometry of EDMs. In: Euclidean Distance Matrices and Their Applications in Rigidity Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-97846-8_5
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DOI: https://doi.org/10.1007/978-3-319-97846-8_5
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