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Spectrum of a matrix
About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.
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TL;DR: In this article, the authors investigated nonperturbative aspects of zero-dimensional matrix models and showed that the tunneling of eigenvalues correspond to a chaotic sequence of recursion coefficients determining the orthogonal polynomials.
Abstract: I investigate non-perturbative aspects of zero-dimensional matrix models. Subtleties in the large-N limit of the semiclassical picture are pointed out. The tunneling of eigenvalues is seen to correspond to a chaotic sequence of recursion coefficients determining the orthogonal polynomials.
01 Jan 2008
TL;DR: The perturbations of Nevanlinna type functions which preserve the set of zeros of this function or add to this set new points are discussed in this article, where the eigenvalues of the perturbed operator are obtained as a set of zero points of the function.
Abstract: The perturbations of Nevanlinna type functions which preserve the set of zeros of this function or add to this set new points are discussed. 1. Statement of the problem The point spectrum in the case of rank one perturbation of purely continuous spectrum may be very rich. In general, this spectrum contains the eigenvalues as well the spectral singularities. We will not give a review of the references (we only indicate (1) and (2)). Let us consider the case where non-perturbed continuous spectrum coincides with the half line (0,1). The eigenvalues of the perturbed operator is obtained as a set of zeros of the function
TL;DR: In this article, a best possible upper bound on the product of the eigenvalues of the closed-loop system is obtained, and the relation between the weighting factors of a quadratic performance criterion and the closed loop system is investigated.
Abstract: Explicit relations between the weighting factors of a quadratic performance criterion and the closed-loop system are developed. A best possible upper bound on the product of the eigenvalues of the closed-loop system is attained.
01 Jan 2005
TL;DR: In this article, another proof of a result of Horn on the existence of a matrix with prescribed singular values and eigenvalues has been given, and it is shown that such a matrix exists.
Abstract: We give another proof of a result of Horn on the existence of a matrix with prescribed singular values and eigenvalues.
Abstract: We consider all of the transmission eigenvalues for one-dimensional media. We give some conditions under which complex eigenvalues exist. In the case when the index of refraction is constant, it is shown that all the transmission eigenvalues are real if and only if the index of refraction is an odd number or reciprocal of an odd number.