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# Eigenvalues and eigenvectors of the second derivative

About: Eigenvalues and eigenvectors of the second derivative is a research topic. Over the lifetime, 579 publications have been published within this topic receiving 17522 citations.

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TL;DR: Exact expressions for rates of change of eigenvalues and eigenvector to facilitate computerized design of complex structures are presented.

Abstract: Exact expressions for rates of change of eigenvalues and eigenvector to facilitate computerized design of complex structures

1,034 citations

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Yale University

^{1}TL;DR: This tutorial will try to provide some intuition as to why these eigenvectors and eigenvalues have combinatorial significance, and will sitn'ey some of their applications.

Abstract: Spectral graph theory is the study of the eigenvalues and eigenvectors of matrices associated with graphs. In this tutorial, we will try to provide some intuition as to why these eigenvectors and eigenvalues have combinatorial significance, and will sitn'ey some of their applications.

665 citations

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TL;DR: In this article, the eigenvectors and eigenvalues of the statistical mean of a random matrix sequence are used for signal processing and pattern recognition, and convergence is shown by stochastic approximation theory.

Abstract: In applications of signal processing and pattern recognition, eigenvectors and eigenvalues of the statistical mean of a random matrix sequence are needed. Iterative methods are suggested and analyzed, in which no sample moments are used. Convergence is shown by stochastic approximation theory.

548 citations

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TL;DR: In this article, the behavior of the eigenvalues of a hermitian matrix under perturbation is studied and two sets of theorems of this sort are given.

Abstract: 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 matrix and those of a matrix approximating it. Two sets of theorems of this sort are given. (auth)

539 citations