Generalized Euclidean distance matrices

Euclidean distance matrices ( ) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized Euclidean distance matrices ( s) that include s. Each is an entry-wise nonnegative matrix. A is not symmetric unless it i...

Full description

Saved in:
Bibliographic Details
Published in:Linear & multilinear algebra 2022-12, Vol.70 (21), p.6908-6929
Main Authors: Balaji, R., Bapat, R.B., Goel, Shivani
Format: Article
Language:English
Subjects:
Eigenvalues
Euclidean distance matrix
Euclidean geometry
Haynsworth inertia formula
infinitely divisible matrices
Laplacian matrices
majorization
Mathematical analysis
Matrices (mathematics)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Euclidean distance matrices ( ) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized Euclidean distance matrices ( s) that include s. Each is an entry-wise nonnegative matrix. A is not symmetric unless it is an . By some new techniques, we show that many significant results on Euclidean distance matrices can be extended to generalized Euclidean distance matrices. These contain results about eigenvalues, inverse, determinant, spectral radius, Moore-Penrose inverse and some majorization inequalities. We finally give an application by constructing infinitely divisible matrices using generalized Euclidean distance matrices.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2021.1972083