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Eigenvalues and Eigenvectors
In this chapter, we explore the foundational concepts of eigenvalues and eigenvectors, providing a deep understanding of their definition,...
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Asymptotic Structure of Eigenvalues and Eigenvectors of Certain Triangular Hankel Matrices
AbstractThe Hankel matrices considered in this article arose in one reformulation of the Riemann hypothesis proposed earlier by the author. Computer...
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Nondegeneracy of eigenvectors and singular vector tuples of tensors
In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications...
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Eigenvalues and Eigenvectors
This chapter deals with the matrix eigenvalue problem, another major theme in linear algebra as important as the theory of linear equations. This...
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Eigenvalues and Eigenvectors
In this chapter we introduce the important notions of eigenvalue and eigenvector of a linear map...
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Generalized eigenvectors of bounded operators
The pseudospectrum and condition spectrum are two essential generalizations of the spectrum. In this paper, we define the eigenvector corresponding...
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Diagonalization: Eigenvalues and Eigenvectors
With diagonalizing matrices we have reached the center of linear algebra. The key to diagonalizing are vectors v not equal to the zero vector with...
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Solved Problems—Eigenvalues and Eigenvectors
Which of the following is an eigenvector of the matrix $$A=\begin{pmatrix} 2...
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High-girth near-Ramanujan graphs with localized eigenvectors
We show that for every prime d and α ∈ (0, 1/6), there is an infinite sequence of ( d + 1)-regular graphs G = ( V, E ) with high girth Ω(α log d (∣ V ∣),...
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Numerical Calculation of Eigenvalues and Eigenvectors
Computation of the eigenvalues λ of a matrix A as zeros of the characteristic polynomial χ A is numerically unstable—small errors in the coefficients...
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Chapter 8: The Distributions of Eigenvalues and Eigenvectors
Our objective in this chapter is to examine the distributions of the eigenvalues and eigenvectors associated with a matrix-variate random variable....
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Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors are introduced by looking for a straight line through the origin which does not move under a linear transformation. It...
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Pseudo-orthogonality for graph 1-Laplacian eigenvectors and applications to higher Cheeger constants and data clustering
The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is an NP-hard problem that can be...
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Tensors with eigenvectors in a given subspace
The first author with B. Sturmfels studied in [
16 ] the variety of matrices with eigenvectors in a given linear subspace, called the Kalman variety.... -
Iterative Methods for Computing Eigenvectors of Nonlinear Operators
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image processing,...
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On power bounded operators with holomorphic eigenvectors. II
In [U] (among other results), M. Uchiyama gave necessary and sufficient conditions for contractions to be similar to the unilateral shift S of...
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Computing the Eigenvectors of Nonsymmetric Tridiagonal Matrices
AbstractThe computation of the eigenvalue decomposition of matrices is one of the most investigated problems in numerical linear algebra. In...
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Approximating the eigenvalues and eigenvectors of birth and death matrices
The objective of this note is to approximate a birth and death matrix B by a close Toeplitz-type one for which explicit formulas for the eigenpairs...
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Approximating Eigenvectors with Fixed-Point Arithmetic: A Step Towards Secure Spectral Clustering
We investigate the adaptation of the spectral clustering algorithm to the privacy preserving domain. Spectral clustering is a data mining technique...