Topic
Spectrum of a matrix
About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.
Papers published on a yearly basis
Papers
More filters
TL;DR: An algorithm due to Jacobs and Trevisan (2011) is applied to study how the number of small Laplacian eigenvalues behaves when the tree is transformed by a transformation defined by Mohar (2007).
21 citations
TL;DR: In this article, the necessary and sufficient conditions for the characteristic roots of a matrix A to lie inside the unit circle are presented, and the following conditions are proved: 1) Linear combinations b i of the coefficients of coefficients of λ √ n of A.
Abstract: In this short paper several theorems related to the necessary and sufficient conditions for the characteristic roots (eigenvalues) of a matrix A to lie inside the unit circle are presented In particular, the following conditions are proved 1) Linear combinations b i of the coefficients of λiin
21 citations
TL;DR: In this article, the Lame operator is studied as complex-analytic function in period τ of an elliptic function and the branching of eigenvalues numerically is investigated.
20 citations
TL;DR: In this paper, the vector initial value problem with stable eigenvalues and zero eigen values having simple elementary divisors is considered and the unique limiting solution is determined when the reduced problem is solvable and a uniform asymptotic expansion for the solution on finite t intervals.
Abstract: Consider the vector initial value problem with for a singular matrix F(t) of constant rank with stable eigenvalues and zero eigenvalues having simple elementary divisors. This paper shows how to determine the unique limiting solution when the reduced problem is solvable and how to obtain a uniform asymptotic expansion for the solution on finite t intervals.
20 citations