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On generalized inverses of singular matrix pencils
 International Journal of Applied Mathematics and Computer Science
, 2011
"... Linear timeinvariant networks are modelled by linear differentialalgebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass struct ..."
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Cited by 1 (0 self)
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structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate singular matrix pencils. The relations between the Kronecker structure of a singular matrix pencil and the multiplicity of poles at zero of the Moore–Penrose inverse and the Drazin inverse of the rational
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 555 (22 self)
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toimplement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank. The algorithm is iterative and produces a sequence of matrices {X k, Y k} and at each step, mainly performs a softthresholding operation on the singular values of the matrix Y k. There are two
Reduction Theorem on Singular Matrix with Special Properties
"... This paper presents how a singular matrix of order n×n formulated using special properties to its immediate low order n1×n1 and we have also found that any square matrix taken randomly from an n×n special properties ’ singular matrix is also singular. This work shows the results of various operati ..."
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This paper presents how a singular matrix of order n×n formulated using special properties to its immediate low order n1×n1 and we have also found that any square matrix taken randomly from an n×n special properties ’ singular matrix is also singular. This work shows the results of various
Orbit Closures of Singular Matrix Pencils
 J. Pure Appl. Algebra
, 1992
"... Equivalence of matrix pencils (pairs of p\Thetaq matrices over C ) is given by the GL p \ThetaGL q action of simultaneous left and right multiplication. The orbits under this group action were described by Kronecker in 1890 in terms of pencil invariants: column indices, row indices, and elementary ..."
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Cited by 11 (2 self)
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Equivalence of matrix pencils (pairs of p\Thetaq matrices over C ) is given by the GL p \ThetaGL q action of simultaneous left and right multiplication. The orbits under this group action were described by Kronecker in 1890 in terms of pencil invariants: column indices, row indices, and elementary
A multilinear singular value decomposition
 SIAM J. Matrix Anal. Appl
, 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are ..."
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Cited by 472 (22 self)
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Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc
Linearizations of singular matrix polynomials and the recovery of minimal indices
, 2009
"... A standard way of dealing with a regular matrix polynomial P(λ) is to convert it into an equivalent matrix pencil – a process known as linearization. Two vector spaces of pencils L1(P) and L2(P) that generalize the first and second companion forms have recently been introduced by Mackey, Mackey, M ..."
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Cited by 23 (10 self)
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, Mehl and Mehrmann. Almost all of these pencils are linearizations for P (λ) when P is regular. The goal of this work is to show that most of the pencils in L1(P)andL2(P)arestill linearizations when P (λ) is a singular square matrix polynomial, and that these linearizations can be used to obtain
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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and the eigenvalue problem. Key words. perturbation theory, random matrix, linear system, least squares, eigenvalue, eigenvector, invariant subspace, singular value AMS(MOS) subject classifications. 15A06, 15A12, 15A18, 15A52, 15A60 1. Introduction. Let A be a matrix and let F be a matrix valued function of A
Results 1  10
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4,333