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1992
Unless otherwise noted, we will assume throughout this chapter that all vector spaces are finite dimensional.
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Unless otherwise noted, we will assume throughout this chapter that all vector spaces are finite dimensional.
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2011
Let \(\mathcal{L}\) be a linear space, \({\mathcal{L}}_{1}\) be a linear subspace of \(\mathcal{L}\) and A be a linear operator in \(\mathcal{L}\). In general, for any vector \(\mathbf{x} \in {\mathcal{L}}_{1}\), A x may not belong to \({\mathcal{L}}_{1}\).
Hasan Ersel +2 more
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Let \(\mathcal{L}\) be a linear space, \({\mathcal{L}}_{1}\) be a linear subspace of \(\mathcal{L}\) and A be a linear operator in \(\mathcal{L}\). In general, for any vector \(\mathbf{x} \in {\mathcal{L}}_{1}\), A x may not belong to \({\mathcal{L}}_{1}\).
Hasan Ersel +2 more
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1996
As mentioned in the previous chapter, besides the significance of matrix simplification through elimination, it is often important to simplify a matrix by preserving its eigenvalues. Eigenvalues and their associated eigenvectors are useful in a variety of situations.
Anastasios A. Tsonis, James B. Elsner
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As mentioned in the previous chapter, besides the significance of matrix simplification through elimination, it is often important to simplify a matrix by preserving its eigenvalues. Eigenvalues and their associated eigenvectors are useful in a variety of situations.
Anastasios A. Tsonis, James B. Elsner
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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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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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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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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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