Results 291 to 300 of about 177,680 (311)
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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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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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