Balaji, R. ; Bapat, R. B.
(2004)
*Block distance matrices*
The Electronic Journal of Linear Algebra, 16
.
pp. 435-443.
ISSN 1081-3810

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Official URL: http://www.emis.ams.org/journals/ELA/ela-articles/...

## Abstract

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by D_{ij} = F_{ii}+F_{jj}-2F_{ij}. When each block in F is 1×1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interesting properties of Euclidean distance matrices to block distance matrices are extended in this paper. Finally, distance matrices of trees with matrix weights are investigated.

Item Type: | Article |
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Source: | Copyright of this article belongs to The European Mathematical Information Service. |

Keywords: | Distance Matrices; Laplacian Matrices; Trees |

ID Code: | 81603 |

Deposited On: | 07 Feb 2012 05:11 |

Last Modified: | 07 Feb 2012 05:11 |

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