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- W2077002005 abstract "If A is a real symmetric matrix and P is an orthogonal projection onto a hyperplane, then we derive a formula for the Moore–Penrose inverse of PAP. As an application, we obtain a formula for the Moore–Penrose inverse of an Euclidean distance matrix (EDM) which generalizes formulae for the inverse of a EDM in the literature. To an invertible spherical EDM, we associate a Laplacian matrix (which we define as a positive semidefinite n × n matrix of rank n − 1 and with zero row sums) and prove some properties. Known results for distance matrices of trees are derived as special cases. In particular, we obtain a formula due to Graham and Lovász for the inverse of the distance matrix of a tree. It is shown that if D is a nonsingular EDM and L is the associated Laplacian, then D−1 − L is nonsingular and has a nonnegative inverse. Finally, infinitely divisible matrices are constructed using EDMs." @default.
- W2077002005 created "2016-06-24" @default.
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- W2077002005 date "2007-07-01" @default.
- W2077002005 modified "2023-09-30" @default.
- W2077002005 title "On Euclidean distance matrices" @default.
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- W2077002005 doi "https://doi.org/10.1016/j.laa.2006.05.013" @default.
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