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Intermediate scattering function of colloids in a periodic laser field.
Soft MatterRusch R +4 more
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High-dimensional neuronal activity from low-dimensional latent dynamics: a solvable model
Schmutz V +5 more
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1986
Recall that an n × n matrix B is similar to an n × n matrix A if there is an invertible n × n matrix P such that B = P −1 AP. Our objective now is to determine under what conditions an n × n matrix is similar to a diagonal matrix. In so doing we shall draw together all of the notions that have been previously developed.
T. S. Blyth, Edmund F. Robertson
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Recall that an n × n matrix B is similar to an n × n matrix A if there is an invertible n × n matrix P such that B = P −1 AP. Our objective now is to determine under what conditions an n × n matrix is similar to a diagonal matrix. In so doing we shall draw together all of the notions that have been previously developed.
T. S. Blyth, Edmund F. Robertson
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The Distribution of the Eigenvalues
1991It follows from the results of Chapter 3 that if the function q(x) of the Sturm-Liouville operator $$ {L_y} = - y'' + q(x)y,\,a < x < , $$ (1.1) is bounded from below, and tends to +∞ as x → a or x → b (or both), then the spectrum of L is discrete (assuming that at least one of the endpoints is singular; furthermore, if at least one of them ...
B. M. Levitan, I. S. Sargsjan
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On the higher eigenvalues for the $\infty$ -eigenvalue problem
Calculus of Variations and Partial Differential Equations, 2005We study the higher eigenvalues and eigenfunctions for the so-called $\infty$ -eigenvalue problem. The problem arises as an asymptotic limit of the nonlinear eigenvalue problems for the p-Laplace operators and is very closely related to the geometry of the ...
Peter Lindqvist, Petri Juutinen
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1966
Publisher Summary This chapter focuses on eigenvalue problems. Eigenvalue problems arise in a number of different areas of mathematics. The differential equation and the boundary conditions constitute an eigenvalue problem. In an eigenvalue problem, associated with a linear homogeneous differential equation of arbitrary order n, each linear ...
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Publisher Summary This chapter focuses on eigenvalue problems. Eigenvalue problems arise in a number of different areas of mathematics. The differential equation and the boundary conditions constitute an eigenvalue problem. In an eigenvalue problem, associated with a linear homogeneous differential equation of arbitrary order n, each linear ...
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2007
Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space.
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Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space.
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1987
In this chapter we describe numerical techniques for the calculation of a scalar λ and non-zero vector x in the equation $$ Ax = \lambda x $$ (4.1) where A is a given n × n matrix. The quantities λ and x are usually referred to as an eigenvalue and an eigenvector of A.
Colin Judd, Ian Jacques
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In this chapter we describe numerical techniques for the calculation of a scalar λ and non-zero vector x in the equation $$ Ax = \lambda x $$ (4.1) where A is a given n × n matrix. The quantities λ and x are usually referred to as an eigenvalue and an eigenvector of A.
Colin Judd, Ian Jacques
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Eigenvectors and Eigenvalues [PDF]
, 1986 This chapter gives the basic elementary properties of eigenvectors and eigenvalues. We get an application of determinants in computing the characteristic polynomial. In §3, we also get an elegant mixture of calculus and linear algebra by relating eigenvectors with the problem of finding the maximum and minimum of a quadratic function on the sphere ...
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1997
The decomposition of a matrix A into a product of two or three matrices can (depending on the characteristics of those matrices) be a very useful first step in computing such things as the rank, the determinant, or an (ordinary or generalized) inverse (of A) as well as a solution to a linear system having A as its coefficient matrix.
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The decomposition of a matrix A into a product of two or three matrices can (depending on the characteristics of those matrices) be a very useful first step in computing such things as the rank, the determinant, or an (ordinary or generalized) inverse (of A) as well as a solution to a linear system having A as its coefficient matrix.
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