Balaji, R. ; Bapat, R. B.
(2007)
*On Euclidean distance matrices*
Linear Algebra and its Applications, 424
(1).
pp. 108-117.
ISSN 0024-3795

Full text not available from this repository.

Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.laa.2006.05.013

## 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 Lovàsz 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.

Item Type: | Article |
---|---|

Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Distance Matrices; Laplacian; Trees; Infinitely Divisible Matrices |

ID Code: | 81579 |

Deposited On: | 07 Feb 2012 05:11 |

Last Modified: | 07 Feb 2012 05:11 |

Repository Staff Only: item control page