In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of ...

Recurrent neural network attractors have the potential to act as state systems, automata, and turing-complete computers. Therefore, a better understanding of these attractors could shed light on how ...

We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees.

The eigenvalues of the normalized Laplacian matrix of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and ...

Ky Fan trace theorems and the interlacing theorems of Cauchy and Poincaré are important observations that characterize Hermitian matrices. In this note, we introduce a new type of inequalities which ...

Understanding eigenvalues and the sum of matrices is crucial for various fields, including data science, machine learning, and engineering. This knowledge allows you to analyze complex systems, solve ...

Department of Molecular Systems Biology, University of Vienna, Vienna, Austria. Mathematical modeling of biochemical systems aims at improving the knowledge about complex regulatory networks. The ...

Abstract: The purpose of this paper is to give a survey of the progress, advantages and limitations of various locating methods of complex matrices' eigenvalues. Some new methods of locating complex ...

Abstract: Simple bounds are presented on the extreme eigenvalues of n*n-dimensional Hermitian Toeplitz matrices. Such a matrix, say T/sub n/, is determined by its first row. The proposed bounds have ...