Related papers: Eigenvectors from eigenvalues revisited
A remarkable mathematical property -- somehow hidden and recently rediscovered -- allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. That opens the possibility to get the wavefunctions from the…
This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850
The main focus of this work is the study of several cones relating the eigenvalues or singular values of a matrix to those of its off-diagonal blocks.
We give a new proof of Theorem 6 in [L. Qiu and X. Zhan, On the span of Hadamard products of vectors, Linear Algebra Appl. 422 (2007) 304--307].
The recent Letter by Bender, Berry, and Mandilara (2002, BBM) presents some interesting symmetry arguments which enable one to transform non-hermitian, PT invariant, (complex) polynomial potential hamiltonians, into secular equation…
In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].
Let $A$ be a fixed complex matrix and let $u,v$ be two vectors. The eigenvalues of matrices $A+\tau uv^\top $ $(\tau\in\mathbb{R})$ form a system of intersecting curves. The dependence of the intersections on the vectors $u,v$ is studied.
Discussion on "Brownian distance covariance" by G\'abor J. Sz\'ekely and Maria L. Rizzo [arXiv:1010.0297]
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
Recently developed applications in the field of machine learning and computational physics rely on automatic differentiation techniques, that require stable and efficient linear algebra gradient computations. This technical note provides a…
We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.
We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzd\c{e}ga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduce several new techniques that have…
I propose a proof of the existence of the existence of eigenvectors and eigenvalues in the spirit of Argand's proof of the fundamental theorem of algebra. The proof only relies on Weierstrass's theorem, the definition of the inverse of a…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
This is a complement to our paper arXiv:0802.1461. We study irreducibility of spectral determinants of some one-parametric eigenvalue problems in dimension one with polynomial potentials.
In this note we provide proofs of various expressions for expectation values of symmetric polynomials in $\beta$-deformed eigenvalue models with quadratic, linear, and logarithmic potentials. The relations we derive are also referred to as…
L.A. Bunimovich and B.Z. Webb developed a theory for isospectral graph reduction. We make a simple observation regarding the relation between eigenvectors of the original graph and its reduction, that sheds new light on this theory. As an…