Results 21 to 30 of about 50 (43)
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1993
This chapter introduces and, to a limited extent, solves one of the classical problems associated with linear processes: their decomposition into well-behaved, independent component subprocesses. What is especially noteworthy and exciting about the material is that it uses all of the major concepts introduced so far, including the representation of ...
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This chapter introduces and, to a limited extent, solves one of the classical problems associated with linear processes: their decomposition into well-behaved, independent component subprocesses. What is especially noteworthy and exciting about the material is that it uses all of the major concepts introduced so far, including the representation of ...
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2000
The search for eigenvalues and eigenvectors of a linear map f, those scalars λ and the non-zero vectors u such that f(u)=λu, is of considerable importance in linear algebra, as well as in the application of mathematics to economics, physics, and engineering.
Jean Michel F, Henri L, George C. D
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The search for eigenvalues and eigenvectors of a linear map f, those scalars λ and the non-zero vectors u such that f(u)=λu, is of considerable importance in linear algebra, as well as in the application of mathematics to economics, physics, and engineering.
Jean Michel F, Henri L, George C. D
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2018
Consider the linear operator T on \({\mathbb {R}}^3\) defined by $$T(a,b,c)=(a+b,b+c,c+a)\quad \text{ for } (a,b, c)\in {\mathbb {R}}^3.$$
M. Thamban Nair, Arindama Singh
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Consider the linear operator T on \({\mathbb {R}}^3\) defined by $$T(a,b,c)=(a+b,b+c,c+a)\quad \text{ for } (a,b, c)\in {\mathbb {R}}^3.$$
M. Thamban Nair, Arindama Singh
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Approximation of Eigenvalues and Eigenvectors
2006In this chapter we deal with approximations of the eigenvalues and eigen-vectors of a matrix A ∈ ℂn×n Two main classes of numerical methods exist to this purpose, partial methods, which compute the extremal eigen-values of A (that is, those having maximum and minimum module), or global methods, which approximate the whole spectrum of A.
Alfio Quarteroni +2 more
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On the rhotrix eigenvalues and eigenvectors
Afrika Matematika, 2012The concept of rhotrix eigenvector eigenvalue problem (REP) was introduced by Aminu (Int. J. Math. Educ. Sci. Technol. 41:98–105, 2010). As an extension to this, we have presented in this article some properties of rhotrix eigenvalues and eigenvectors considering the numerous applications of matrix eigenvector eigenvalue problem in areas of Applied ...
S. Usaini, L. Mohammed
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1996
Let a ∈ and a ≠0. Prove that the eigenvectors of the matrix $$ \left( {\begin{array}{*{20}c} 1 & a \\ 0 & 1 \\ \end{array} } \right) $$ generate a 1-dimensional space, and give a basis for this space.
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Let a ∈ and a ≠0. Prove that the eigenvectors of the matrix $$ \left( {\begin{array}{*{20}c} 1 & a \\ 0 & 1 \\ \end{array} } \right) $$ generate a 1-dimensional space, and give a basis for this space.
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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 of Matrices
1996For a given (n, n) matrix A = (a ik ) the eigenvalue problem consists of finding nonzero vectors x so that A x is parallel to the vector x. Such a vector x is called an eigenvector of A. It satisfies the eigenvalue-eigenvector equation for a scalar λ, called the eigenvalue: $$ Ax = \lambda x. $$ (7.1)
Frank Uhlig, Gisela Engeln-Müllges
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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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