Results 11 to 20 of about 38,752 (314)
Convergence of Eigenvector Continuation [PDF]
Phys. Rev. Lett. 126, 032501 (2021), 2020 Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to selected training values of the control parameters.
Avik Sarkar, Dean Lee
arxiv +6 more sources
On Differentiating Eigenvalues and Eigenvectors [PDF]
Econometric Theory, 1985 Let X0 be a square matrix (complex or otherwise) and u0 a (normalized) eigenvector associated with an eigenvalue λo of X0, so that the triple (X0, u0, λ0) satisfies the equations Xu = λu, . We investigate the conditions under which unique differentiable functions λ(X) and u(X) exist in a neighborhood of X0 satisfying λ(X0) = λO, u(X0) = u0, Xu = λu ...
Jan R. Magnus
openalex +7 more sources
The American Mathematical Monthly, 2022 The recursively-constructed family of Mandelbrot matrices $M_n$ for $n=1$, $2$, $\ldots$ have nonnegative entries (indeed just $0$ and $1$, so each $M_n$ can be called a binary matrix) and have eigenvalues whose negatives $-λ= c$ give periodic orbits under the Mandelbrot iteration, namely $z_k = z_{k-1}^2+c$ with $z_0=0$, and are thus contained in the ...
Neil J. Calkin +4 more
openaire +2 more sources
The rotation of eigenvectors by a perturbation—II
Journal of Mathematical Analysis and Applications, 1965 Although the behavior of the eigenvalues of a hermitian matrix under perturbation is fairly well understood, there has been almost nothing done on the behavior of the eigenvectors. It is well known that they vary analytically under analytic perturbations but for some purposes one would prefer sharp bounds on the distance between the eigenvectors of a ...
Chandler Davis
openalex +3 more sources
Eigenvectors of Permutation Matrices [PDF]
Advances in Pure Mathematics, 2015 The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polynomial, and a set of linearly independent eigenvectors from the decomposition in disjoint cycles of the permutation ...
García Planas, María Isabel +1 more
openaire +4 more sources
All opinions are not equal: Toward a consensual approach to the development of drug policy
Australian Journal of Social Issues, Volume 57, Issue 4, Page 812-828, December 2022., 2022 Abstract Drug policy has been subjected to much scrutiny from different stakeholder groups who present sometimes very different opinions on solutions to address a problem. Reconciling such differences, that are underpinned by both anecdotal and empirical evidence, is a priority yet to be fully achieved.
Gabriel T. W. Wong, Matthew Manning
wiley +1 more source
Eigenvectors and Reconstruction [PDF]
The Electronic Journal of Combinatorics, 2007 In this paper, we study the simple eigenvectors of two hypomorphic matrices using linear algebra. We also give new proofs of results of Godsil and McKay.
openaire +3 more sources
Discrete-time population dynamics on the state space of measures
Mathematical Biosciences and Engineering, 2020 If the individual state space of a structured population is given by a metric space S, measures μ on the σ-algebra of Borel subsets T of S offer a modeling tool with a natural interpretation: μ(T) is the number of individuals with structural ...
Horst R. Thieme
doaj +1 more source
Morphologies in‐between: The impact of the first steps on the human talus
The Anatomical Record, Volume 306, Issue 1, Page 124-142, January 2023., 2023 Abstract Objective The development of bipedalism is a very complex activity that contributes to shaping the anatomy of the foot. The talus, which starts ossifying in utero, may account for the developing stages from the late gestational phase onwards.
Carla Figus +21 more
wiley +1 more source
Controllability of Brain Neural Networks in Learning Disorders—A Geometric Approach
Mathematics, 2022 The human brain can be interpreted mathematically as a linear dynamical system that shifts through various cognitive regions promoting more or less complicated behaviors. The dynamics of brain neural network play a considerable role in cognitive function
Maria Isabel García-Planas +1 more
doaj +1 more source