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.
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TL;DR: In this paper, the exact eigenvalues and eigenfunctions of systems of the form (l) were obtained for the case v = 0, using a technique similar to one employed by Boyer [2] to treat the case V = 0.
TL;DR: This paper presents an explicit construction of a decreasing sequence of disk centered at ml¸ in such a way that each disk in the sequence contains all the eigenvalues for a complex matrix A.
Abstract: This paper presents an explicit construction of a decreasing sequence of disk centered at m¸ in such a way that each disk in the sequence contains all the eigenvalues for a complex matrix A. Our sequence complement a decreasing sequence of rectangles obtained by O. Rojo, R. Soto and H. Rojo in matrix with complex entries can be made with no knowledge of the eigenvalues of the matrix.
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TL;DR: In this paper, the authors derive inequalities for sums of eigenvalues of Schr\"{o}dinger operators on finite intervals and tori, and show that the inequalities converge to the classical trace formulae in the limit as the number of eigvalues considered approaches infinity.
Abstract: We derive inequalities for sums of eigenvalues of Schr\"{o}dinger operators on finite intervals and tori. In the first of these cases, the inequalities converge to the classical trace formulae in the limit as the number of eigenvalues considered approaches infinity.
10 Nov 2022
TL;DR: In this article , the intelligent application of matrix eigenvalues and eigenvalue methods based on tensor analysis is studied, in order for students to have a deep understanding of eigen values and Eigenvectors from multiple perspectives.
Abstract: This paper firstly studies the intelligent application of matrix eigenvalues and eigenvalue methods based on tensor analysis. Then, starting from the concept of eigenvalues and eigenvectors and the eigenvalue decomposition theorem, through intuitive geometric demonstration, eigenvalue deployment and high-dimensional data Two specific examples of dimensionality reduction, combined with MATLAB software to clarify the geometric intuition and practical application of eigenvalues and eigenvectors, in order for students to have a deep understanding of eigenvalues and eigenvectors from multiple perspectives.
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TL;DR: In this paper, the eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic R matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic field smaller than the critical value.
Abstract: The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the elliptic R matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic field smaller than the critical value. An argument based on generating functions is given, and the results are checked numerically. The spectrum consists of equally spaced levels. IMAFF 93/13