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43
Antitriangular and antimHessenberg forms for Hermitian matrices and pencils
"... Mehly Hermitian pencils, i.e., pairs of Hermitian matrices, arise in many applications, such as linear quadratic optimal control or quadratic eigenvalue problems. We derive conditions from which antitriangular and antimHessenberg forms for general (including singular) Hermitian pencils can be ob ..."
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Mehly Hermitian pencils, i.e., pairs of Hermitian matrices, arise in many applications, such as linear quadratic optimal control or quadratic eigenvalue problems. We derive conditions from which antitriangular and antimHessenberg forms for general (including singular) Hermitian pencils can
Antitriangular and antimHessenberg forms for Hermitian matrices and pencils
, 1999
"... Hermitian pencils, i.e., pairs of Hermitian matrices, arise in many applications, such as linear quadratic optimal control or quadratic eigenvalue problems. We derive conditions which antitriangular and antimHessenberg forms for general (including singular) Hermitian pencils can be obtained under ..."
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Cited by 7 (0 self)
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Hermitian pencils, i.e., pairs of Hermitian matrices, arise in many applications, such as linear quadratic optimal control or quadratic eigenvalue problems. We derive conditions which antitriangular and antimHessenberg forms for general (including singular) Hermitian pencils can be obtained
Definite matrix polynomials and their linearization by definite pencils
 Manchester Institute for Mathematical Sciences, The University of Manchester
, 2008
"... Abstract. Hyperbolic matrix polynomials are an important class of Hermitian matrix polynomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that their eigenvalues are real and semisimple. We extend the definition of hyperbolic matrix po ..."
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Cited by 14 (7 self)
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Abstract. Hyperbolic matrix polynomials are an important class of Hermitian matrix polynomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that their eigenvalues are real and semisimple. We extend the definition of hyperbolic matrix
On the intersection of Hermitian surfaces
"... In [6] and [3] the authors determine the structure of the intersection of two Hermitian surfaces of PG(3, q 2) under the hypotheses that in the pencil they generate there is at least one degenerate surface. In [1] and [3] it is shown that under suitable hypotheses the intersection of two Hermitian s ..."
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Cited by 1 (0 self)
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In [6] and [3] the authors determine the structure of the intersection of two Hermitian surfaces of PG(3, q 2) under the hypotheses that in the pencil they generate there is at least one degenerate surface. In [1] and [3] it is shown that under suitable hypotheses the intersection of two Hermitian
On perturbations of matrix pencils with real spectra
 Mathematics of Computation
, 1994
"... Abstract. A wellknown result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A and �A be two n × n Hermitian matrices, and let λ1,...,λn and �λ1,...,�λn be their eigenvalues arranged in ascending order. Then � � � � � �diag(λ1 − �λ1,...,λn −�λn) � � � � � � ..."
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Cited by 13 (7 self)
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Abstract. A wellknown result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A and �A be two n × n Hermitian matrices, and let λ1,...,λn and �λ1,...,�λn be their eigenvalues arranged in ascending order. Then � � � � � �diag(λ1 − �λ1,...,λn −�λn
ISSN 17499097DEFINITE MATRIX POLYNOMIALS AND THEIR LINEARIZATION BY DEFINITE PENCILS ∗
, 2007
"... Abstract. Hyperbolic matrix polynomials are an important class of Hermitian matrix polynomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that their eigenvalues are real and semisimple. We extend the definition of hyperbolic matrix po ..."
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Abstract. Hyperbolic matrix polynomials are an important class of Hermitian matrix polynomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that their eigenvalues are real and semisimple. We extend the definition of hyperbolic matrix
A perturbation bound for definite pencils
 Linear Algebra Appl
, 1993
"... We attempt to generalize a wellknown result on spectral variations of a Hermitian matrix due to Mirsky to the definite generalized eigenvalue problem. We also point out that some results on perturbations of definite pencils due to Stewart can be slightly improved. 1. ..."
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Cited by 2 (0 self)
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We attempt to generalize a wellknown result on spectral variations of a Hermitian matrix due to Mirsky to the definite generalized eigenvalue problem. We also point out that some results on perturbations of definite pencils due to Stewart can be slightly improved. 1.
Optimizing Eigenvalues of Symmetric Definite Pencils
 in Proceedings of the 1994 American Control Conference
, 1994
"... We consider the following quasiconvex optimization problem: minimize the largest eigenvalue of a symmetric definite matrix pencil depending on parameters. A new form of optimality conditions is given, emphasizing a complementarity condition on primal and dual matrices. Newton's method is then a ..."
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Cited by 7 (0 self)
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: minimize the maximum eigenvalue of the Hermitian definite pencil (A(x); B(x)), w.r.t. a parameter vector x, subject to positive definite constraints on B(x) and sometimes also on other Hermitian matrix functions of x. The maximum eigenvalue is a quasiconvex function of the pencil elements and therefore
Canonical Forms for Doubly Structured Matrices and Pencils
, 2000
"... In this paper we derive canonical forms under structure preserving equivalence transformations for matrices and matrix pencils that have a multiple structure, which is either an Hselfadjoint or Hskewadjoint structure, where the matrix H is a complex nonsingular Hermitian or skewHermitian matrix. ..."
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Cited by 17 (0 self)
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In this paper we derive canonical forms under structure preserving equivalence transformations for matrices and matrix pencils that have a multiple structure, which is either an Hselfadjoint or Hskewadjoint structure, where the matrix H is a complex nonsingular Hermitian or skewHermitian matrix
Results 1  10
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