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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
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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
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Eigenvectors in bottleneck algebra
Linear Algebra and its Applications, 1992 The paper deals with a characterization of the eigenvectors in terms of the associated graph and with an alternative way of computing them. Upper and lower bounds for all eigenvectors are given. The approach is illustrated by several numerical examples.
Kataŕına Cechlárová
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Applied Sciences, 2023 The calculation of accurate arbitrary-order sensitivities of eigenvalues and eigenvectors is crucial for structural analysis applications, including topology optimization, system identification, finite element model updating, damage detection, and fault ...
Juan C. Velasquez-Gonzalez +5 more
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Portfolio Optimization and Random Matrix Theory in Stock Exchange [PDF]
مدیریت نوآوری و راهبردهای عملیاتی, 2021 Purpose: This study aimed to optimize the stock portfolio based on stochastic matrix theory in the stock market and to answer whether the relevant information will exist using the Marčenko–Pastur distribution.Methodology: The data of 31 shares in the ...
mostafa heidari haratemeh
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Using principal eigenvectors of Laplacian-Plus matrix to identify spreaders of social networks under linear threshold diffusion model [PDF]
AUT Journal of Mathematics and Computing, 2022 Influence maximization (IM) is a challenging problem in social networks to identify initial spreaders with the best influence on other nodes. It is a need to solve this problem with the minimum diffusion time and the most coverage on the communities ...
Neda Binesh, Mehdi Ghatee
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Lietuvos Matematikos Rinkinys, 2023 Investigation of the mutual synchronizatin system with delays, composed of n (n= 2p +1, p ∈ N) oscillators joined into a onedirectional ring, is carried out.
Gintarė Leonaitė, Jonas Rimas
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An Improved Kinect Recognition Method for Identifying Unsafe Behaviors of Metro Passengers
Sensors, 2022 In order to solve the problem of the low action recognition accuracy of passengers’ unsafe behaviors caused by redundant joints, this study proposes an efficient recognition method based on a Kinect sensor.
Ying Lu +3 more
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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
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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
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