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Eigenvalues and Eigenvectors of Matrices [PDF]
, 1995 Throughout this chapter we will consider square matrices only. We shall see that many properties of an n × n matrix A can be understood by determining which (if any) vectors \( \vec{\upsilon } \in {{R}^{n}} \) ∈ R n satisfy \( A\vec{\upsilon } = k\vec{\upsilon } \) for some real number k.
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Eigenvalues and eigenvectors in GaAs
Journal of Molecular Structure, 1991Abstract A simple 11-parameter rigid-ion model (RIM) is used to describe the recent additional phonon dispersion curves of GaAs measured by the neutron scattering technique. Contrary to various claims in the literature, it is shown here, that when an optimized set of force constant parameters of this model are used for GaAs, the model predicts both ...
C. Patel, T.J. Parker, W.F. Sherman
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1975
We have already seen, in chapter 2, that if A is square and nonsingular a unique solution of the equation Ax = b exists for any arbitrary b. Equations of this form arise frequently when analysing the static behaviour of physical and economics systems and often represent the response of the system to the particular set of applied stimuli embodied in the
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We have already seen, in chapter 2, that if A is square and nonsingular a unique solution of the equation Ax = b exists for any arbitrary b. Equations of this form arise frequently when analysing the static behaviour of physical and economics systems and often represent the response of the system to the particular set of applied stimuli embodied in the
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Matrices, Eigenvalues and Eigenvectors
2014Many complex mathematical problems can be formulated as eigenvalue problems. In Exercises 3.1 and 3.2 examples are given where direct computation of eigenvalues and eigenspaces can be carried out. In Exercise 3.3 we show how the eigenvalues of a matrix and its inverse are related, while the eigenvalues of a positive definite matrix are considered in ...
Jean-Louis Merrien, Tom Lyche
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Evaluation of Eigenvalues and Eigenvectors
2017Before we discuss methods for computing eigenvalues, we recall a remark made in Chap. 5 A given nth-degree polynomial p(c) is the characteristic polynomial of some matrix. The companion matrix of equation ( 3.225) is one such matrix.
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The elements of eigenvalue and eigenvector theory
1978Suppose that $$ {\text{T}}:V \to V $$ is a linear transformation of the vector space V to itself. Such linear transformations have a special name (because their domain and range space are the same), they are called endomorphisms of V.
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Eigenvalue-Eigenvector Solution
1985In this chapter, methods are presented for solving the free vibration equation for a multi-degree of freedom system. This equation is called the eigenvalue equation. Its solution not only gives the natural frequencies and mode shapes but also allows the set of coupled equations representing the dynamic response of a system to be uncoupled and hence ...
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Eigenvalues and Eigenvectors of the KBE
1977Consider the KBE $$\frac{{\partial u}}{{\partial t}} = Au$$ (7.1) where $$u = u(t,x) = \int_0^1 {p(t,x,y)f(y)dy.}$$ (7.2)
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