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On the second real eigenvalue of nonnegative and Zmatrices
 LINEAR ALGEBRA APPL
, 1997
"... We give bounds for the second real eigenvalue of nonnegative matrices and Zmatrices. Furthermore, we establish upper bounds for the maximal spectral radii of principal submatrices of nonnegative matrices. Using this bounds we prove that our inequality for the second real eigenvalue of the inciden ..."
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Cited by 5 (2 self)
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We give bounds for the second real eigenvalue of nonnegative matrices and Zmatrices. Furthermore, we establish upper bounds for the maximal spectral radii of principal submatrices of nonnegative matrices. Using this bounds we prove that our inequality for the second real eigenvalue
Characterization of Sign Controllability for Linear Systems with Real Eigenvalues
"... Abstract — A linear timeinvariant system of the form ˙x(t) = Ax(t) + Bu(t), or x(t + 1) = Ax(t) + Bu(t) is sign controllable if all linear timeinvariant systems whose matrices A ′ and B ′ have the same sign pattern as A and B are controllable. This work characterizes the sign controllability for ..."
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Cited by 1 (1 self)
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for systems, whose sign pattern of A allows only real eigenvalues. Moreover, we present a combinatorial condition which is necessary for sign controllability and we show that if this condition is satisfied, then in all linear timeinvariant systems with that sign pattern, all real eigenvalues of A
CLASSES OF NONHERMITIAN OPERATORS WITH REAL EIGENVALUES
, 2010
"... Classes of nonHermitian operators that have only real eigenvalues are presented. Such operators appear in quantum mechanics and are expressed in terms of the generators of the WeylHeisenberg algebra. For each nonHermitian operator A, a Hermitian involutive operator ˆ J such that A is ˆJHermiti ..."
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Classes of nonHermitian operators that have only real eigenvalues are presented. Such operators appear in quantum mechanics and are expressed in terms of the generators of the WeylHeisenberg algebra. For each nonHermitian operator A, a Hermitian involutive operator ˆ J such that A is ˆJ
Bounds on real eigenvalues and singular values of interval matrices
 SIAM J. Matrix Anal. Appl
"... Abstract. We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce assharpaspossible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on the one hand such interval matrices h ..."
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Cited by 7 (1 self)
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Abstract. We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce assharpaspossible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on the one hand such interval matrices
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1554 (85 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5pixel products in 16x16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.
Real Eigenvalue of a NonHermitian Hamiltonian System
, 2012
"... With a view to getting further insight into the solutions of onedimensional analogous Schrödinger equation for a nonhermitian (complex) Hamiltonian system, we investigate the quasiexact symmetric solutions for an octic potential and its variant using extended complex phase space approach characte ..."
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on the nature of eigenvalue and eigenfunction of a system. The imaginary part of energy eigenvalue of a nonhermitian Hamiltonian exist for complex potential parameters and reduces to zero for real parameters. However, in the present work, it is found that imaginary component of the energy eigenvalue vanishes
SOME PROPERTIES OF 3 × 3 OCTONIONIC HERMITIAN MATRICES WITH NONREAL EIGENVALUES
, 2000
"... We discuss our preliminary attempts to extend previous work on 2 × 2 Hermitian octonionic matrices with nonreal eigenvalues to the 3 × 3 case. 1. ..."
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We discuss our preliminary attempts to extend previous work on 2 × 2 Hermitian octonionic matrices with nonreal eigenvalues to the 3 × 3 case. 1.
A Parallelizable Eigensolver for Real Diagonalizable Matrices with Real Eigenvalues
, 1991
"... . In this paper, preliminary research results on a new algorithm for finding all the eigenvalues and eigenvectors of a real diagonalizable matrix with real eigenvalues are presented. The basic mathematical theory behind this approach is reviewed and is followed by a discussion of the numerical consi ..."
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Cited by 30 (6 self)
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. In this paper, preliminary research results on a new algorithm for finding all the eigenvalues and eigenvectors of a real diagonalizable matrix with real eigenvalues are presented. The basic mathematical theory behind this approach is reviewed and is followed by a discussion of the numerical
Results 1  10
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256,041