Ela Matrices and Graphs in Euclidean Geometry
نویسنده
چکیده
Some examples of the interplay between matrix theory, graph theory and n-dimensional Euclidean geometry are presented. In particular, qualitative properties of interior angles in simplices are completely characterized. For right simplices, a relationship between the tree of legs and the circumscribed Steiner ellipsoids is proved.
منابع مشابه
Ela Euclidean and Circum-euclidean Distance Matrices: Characterizations and Linear Preservers
Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.
متن کاملEla Block Distance Matrices
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 interes...
متن کاملMatrices and graphs in Euclidean geometry
Some examples of the interplay between matrix theory, graph theory and n-dimensional Euclidean geometry are presented. In particular, qualitative properties of interior angles in simplices are completely characterized. For right simplices, a relationship between the tree of legs and the circumscribed Steiner ellipsoids is proved.
متن کاملEla on Euclidean Distance Matrices of Graphs
Received by the editors on November 13, 2011. Accepted for publication on July 8, 2013. Handling Editor: Bryan L. Shader. FMF and IMFM, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia, and IAM, University of Primorska, Slovenia ([email protected]). XLAB d.o.o., Pot za Brdom 100, 1125 Ljubljana, Slovenia, and FMF, University of Ljubljana, Slovenia ([email protected]...
متن کاملEla Norm Estimates for Functions of Two Commuting
Matrix valued analytic functions of two commuting matrices are considered. A precise norm estimate is established. As a particular case, the matrix valued functions of two matrices on tensor products of Euclidean spaces are explored.
متن کامل