Topic
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.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: In this article, Huang and So gave a complete characterization of the $2\times 2$ symplectic matrices having an infinite number of left eigenvalues, which was later improved by applying an algorithm for the resolution of equations due to De Leo et al.
Abstract: We obtain a complete characterization of the $2\times 2$ symplectic matrices having an infinite number of left eigenvalues. Previously, we give a new proof of a result from Huang and So about the number of eigenvalues of a quaternionic matrix. This is achieved by applying an algorithm for the resolution of equations due to De Leo et al.
TL;DR: In this paper, the 3D eddy-current transient field problem is formulated using the u-v method, which is applied to the FELIX medium cylinder (a conducting cylinder placed in a collapsing external field) and compared to data.
Abstract: The three-dimensional (3-D) eddy-current transient field problem is formulated first using the u-v method. This method breaks the vector Helmholtz equation into two scalar Helmholtz equations. Null-field integral equations and the appropriate boundary conditions germane to the problem are used to set up an identification matrix which is independent of null-field point locations. Embedded in the identification matrix are the unknown eigenvalues of the problem representing its impulse response in time. These eigenvalues are found by equating the determinant of the identification matrix to zero. The eigenvalues, which can be equated with temporal response, are found to be intimately linked to the initial forcing function which triggers the transient in question. When this initial forcing function is Fourier decomposed into its respective spatial harmonics, it is possible to associate with each Fourier component a unique eigenvalue by this technique. The true transient solution comes through a convolution of the impulse response so obtained with the particular imposed external field governing the problem at hand. The technique is applied to the FELIX medium cylinder (a conducting cylinder placed in a collapsing external field) and compared to data. A pseudoanalytic confirmation of the eigenvalues so obtained is formulated to validate the procedure. The technique proposed is applied in the low-frequency regime where the near-field effects must be considered. Application of the technique to a high frequency follows directly if the Coulomb gauge is adopted to represent the vector potential.
23 Aug 2012
TL;DR: In this paper, an improvement on Fan's theorem of matrix eigenvalues was given in terms of Perron roots and Perron vectors of positive (or irreducible nonnegative) matrices.
Abstract: In order to estimate eigenvalues of matrix, an improvement on Ky Fan's theorem of matrix eigenvalues will be given in the article in terms of Perron roots and Perron vectors of positive (or irreducible nonnegative) matrices. At the same time, some examples are shown to test the results.
Posted Content•
TL;DR: This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigen values defined in another Hilbert space based on using the max-min principle for the Eigenvalue problems.
Abstract: This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigenvalues defined in another Hilbert space. The method is based on using the max-min principle for the eigenvalue problems.