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Showing papers on "Spectrum of a matrix published in 1986"


Journal ArticleDOI
TL;DR: In this article, the spectrum of the electrostatic integral operator of a sphere and a prolate spheroid was shown to lie in the interval [−1, 0] and [− 1, 1] of a smooth surface for which the underlying integral operator has a positive eigenvalue.

36 citations


Journal ArticleDOI
TL;DR: In this article, a new type of eigenvalue problem is introduced whose solution provides a spectrum of characteristic exponents for chaotic repellers or semi-attractors, and explicitly tractable examples this spectrum coincides with that of the generalized dimensions.

23 citations



Journal ArticleDOI
TL;DR: In this paper, the authors discuss two dynamical systems on the unit sphere, each defined in terms of a real square matrix M. The solutions of these systems are found to converge to points which provide essential information about eigenvalues of the matrix M and show that the dynamics of the second flow is analogous to that of the Rayleigh quotient iterations.
Abstract: This paper discusses two dynamical systems on the unit sphere $S^{n - 1} $ in $\mathbb{R}^n $ space, each defined in terms of a real square matrix M. The solutions of these systems are found to converge to points which provide essential information about eigenvalues of the matrix M. It is shown, in particular, how the dynamics of the second flow is analogous to that of the Rayleigh quotient iterations.

10 citations


Journal ArticleDOI
TL;DR: In this article, a necessary condition for a positive semi-definite matrix to be a permanent maximizing matrix is that A commute with its permanental adjoint, which is the same condition as in this paper.
Abstract: As a step toward understanding the unsolved problem of determining how large the permanent of a positive semi-definite matrix can be, given the eigenvalues, we note that a necessary condition for A to be a permanent maximizing matrix is that A commute with its permanental adjoint.

7 citations


Journal ArticleDOI
TL;DR: In this paper, it was proved that the mono-energetic transport operator for the case of a spherically-symmetric, isotropically-scattering sphere with a central cavity, has infinitely many complex eigenvalues.
Abstract: In this Letter it is proved that the mono-energetic neutron transport operator for the case of a spherically-symmetric, isotropically-scattering sphere with a central cavity, has infinitely many complex eigenvalues.

4 citations


Journal ArticleDOI
TL;DR: In this paper, a new means for obtaining approximate uniform semiclassical eigenvalues of multi-dimensional systems is examined, where the eigenvalue for a rigid bender model of H 2 O at j = 10 and v = 3 is found to be in good agreement with the corresponding quantum eigen values.

4 citations


Journal ArticleDOI
TL;DR: In this article, the rank of the structure matrix has the values 1,2, or 3; this yields a classification of econometric models, and it turns out that the trace of the (0, 1)-matrices has some interesting properties.

4 citations


Journal ArticleDOI
TL;DR: In this article, an identity satisfied by the eigenvalues of a real-symmetric matrix and an integral representation of a determinant using Grassmann variables is used to show that the ensemble average ofS different pairs of eigen values of a GOE is given by (−1)S2−Sπ−1/2Γ(S + 1/2).
Abstract: An identity satisfied by the eigenvalues of a real-symmetric matrix and an integral representation of a determinant using Grassmann variables are used to show that the ensemble average ofS different pairs of eigenvalues of a GOE is given by (−1)S2−Sπ−1/2Γ(S+1/2).

4 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the matrices AB and BA formed from the product of a positive definite self-adjoint matrix A and a self-adjoint matrix B have real eigenvalues and a complete set of eigenvectors.
Abstract: It is proven that the matrices AB and BA formed from the product a positive definite self-adjoint matrix A and a self-adjoint matrix B has real eigenvalues and a complete set of eigenvectors. If B is positive (negative) semidefinite the eigenvalues are greater (less) than or equal to zero. These properties have been useful in the analysis of multicomponent diffusion and distillation processes.

1 citations



ReportDOI
15 May 1986
TL;DR: In this paper, the spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix.
Abstract: : The spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix. We demonstrate that in many cases knowledge of the eigenvalues alone is sufficient to compute the first passage time distribution.