Results 251 to 260 of about 19,138 (302)
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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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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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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.
George C. D, Jean Michel F, Henri L
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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.
George C. D, Jean Michel F, Henri L
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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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2019
In this chapter we present the main results regarding eigenvalues and eigenvectors of compact and/or symmetric operators. This includes the Hilbert–Schmidt Theorem and its applications to the main eigenvalue problems for the Laplacian.
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In this chapter we present the main results regarding eigenvalues and eigenvectors of compact and/or symmetric operators. This includes the Hilbert–Schmidt Theorem and its applications to the main eigenvalue problems for the Laplacian.
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2010
Given a square matrix \( {\rm A} \in \mathbb{C}^{{n \times n}} \), the eigenvalue problem consists in finding a scalar λ (real or complex) and a nonnull vector x such that $${\rm Ax} = \lambda{\rm x}$$ (6.1) Any such λ is called an eigenvalue of A, while x is the associated eigenvector.
Alfio Quarteroni +2 more
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Given a square matrix \( {\rm A} \in \mathbb{C}^{{n \times n}} \), the eigenvalue problem consists in finding a scalar λ (real or complex) and a nonnull vector x such that $${\rm Ax} = \lambda{\rm x}$$ (6.1) Any such λ is called an eigenvalue of A, while x is the associated eigenvector.
Alfio Quarteroni +2 more
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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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2014
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.
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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.
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1998
Abstract Rather than giving the formal definition of eigenvalues and eigenvectors — the subject of this chapter, indeed of the rest of the book — straight away, we shall give a hypothetical example of their use to motivate their study. We imagine a team of biologists studying a single-celled organism which reproduces by cell division.
Richard Kaye, Robert Wilson
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Abstract Rather than giving the formal definition of eigenvalues and eigenvectors — the subject of this chapter, indeed of the rest of the book — straight away, we shall give a hypothetical example of their use to motivate their study. We imagine a team of biologists studying a single-celled organism which reproduces by cell division.
Richard Kaye, Robert Wilson
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