Results 1 to 10 of about 50 (43)
On Differentiating Eigenvalues and Eigenvectors [PDF]
Econometric Theory, 1985 Let X0 be a square matrix (complex or otherwise) and u0 a (normalized) eigenvector associated with an eigenvalue λo of X0, so that the triple (X0, u0, λ0) satisfies the equations Xu = λu, . We investigate the conditions under which unique differentiable functions λ(X) and u(X) exist in a neighborhood of X0 satisfying λ(X0) = λO, u(X0) = u0, Xu = λu ...
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Eigenvalues and eigenvectors of supermatrices [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1988 On etudie le probleme des valeurs propres des supermatrices d'une facon generale et naturelle en introduisant les notions de (super) valeur propre et vecteur ...
Kobayashi, Yuji, Nagamachi, Shigeaki
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, 1997 The decomposition of a matrix A into a product of two or three matrices can (depending on the characteristics of those matrices) be a very useful first step in computing such things as the rank, the determinant, or an (ordinary or generalized) inverse (of A) as well as a solution to a linear system having A as its coefficient matrix.
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Differentiable roots, eigenvalues, and eigenvectors [PDF]
Israel Journal of Mathematics, 2014 We determine the conditions for the existence of $C^p$-roots of curves of monic complex polynomials as well as for the existence of $C^p$-eigenvalues and $C^p$-eigenvectors of curves of normal complex matrices.
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Tests for Principal Eigenvalues and Eigenvectors
SSRN Electronic JournalWe establish central limit theorems for principal eigenvalues and eigenvectors under a large factor model setting, and develop two-sample tests of both principal eigenvalues and principal eigenvectors. One important application is to detect structural breaks in large factor models.
Fan, Jianqing +3 more
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Eigenvalues and eigenvectors [PDF]
, 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 +3 more
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Some of the next articles are maybe not open access.
2017
This chapter begins with the basic theory of eigenvalues and eigenvectors of matrices. Essential concepts such as characteristic polynomials, the Fundamental Theorem of Algebra, the Gerschgorin circle theorem, invariant subspaces, change of basis, spectral radius and the distance between subspaces are developed.
James R. Kirkwood, Bessie H. Kirkwood
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This chapter begins with the basic theory of eigenvalues and eigenvectors of matrices. Essential concepts such as characteristic polynomials, the Fundamental Theorem of Algebra, the Gerschgorin circle theorem, invariant subspaces, change of basis, spectral radius and the distance between subspaces are developed.
James R. Kirkwood, Bessie H. Kirkwood
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1986
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.
T. S. Blyth, Edmund F. Robertson
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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.
T. S. Blyth, Edmund F. Robertson
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Eigenvectors and Eigenvalues [PDF]
, 1986 This chapter gives the basic elementary properties of eigenvectors and eigenvalues. We get an application of determinants in computing the characteristic polynomial. In §3, we also get an elegant mixture of calculus and linear algebra by relating eigenvectors with the problem of finding the maximum and minimum of a quadratic function on the sphere ...
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