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 article, it has been shown that the τ2 (Baxter-Bazhanov-Stroganov) model for N = 2 with arbitrary parameters is a particular case of the generalized Ising model.
Abstract: It has been shown that the τ2 (Baxter-Bazhanov-Stroganov) model for N = 2 with arbitrary parameters is a particular case of the generalized Ising model. The model satisfies the free-fermion condition, which enables one to solve it by the method of the auxiliary Grassmann field. Explicit expressions have been derived for the partition function on a finite-size lattice and eigenvalues of the transfer matrix. In this approach, in contrast to the functional relation method, there is no problem with the multiplicities of the eigenvalues of transfer matrix.
17 citations
TL;DR: In this paper, the authors considered the case of a perturbation Y of arbitrary finite rank and gave sufficient conditions under which an embedded eigenvalue h, of a self-adjoint operator T, of simple multiplicity vanishes under perturbations by I' (Theorem I), and the main tool in the proof was the formula (1.0.6) for the inverse of the Weinstein-Aronszajn matrix W(z).
17 citations
TL;DR: In this paper, the directional derivatives of multiple eigenvalues of a symmetric eigenproblem analytically dependent on several parameters are given, and the result can be used to define the sensitivity of multiple Eigenvalues, and it is useful for investigating structural vibration design and control system design.
Abstract: This note is a continuation of the work in [J. Comput. Math., 6 (1988), pp. 28–38]. The directional derivatives of multiple eigenvalues of a symmetric eigenproblem analytically dependent on several parameters are given. The result can be used to define the sensitivity of multiple eigenvalues, and it is useful for investigating structural vibration design and control system design.
17 citations
17 citations
TL;DR: In this paper, the authors compared the Smith normal form (SNF) over the integers of an integral nonsingular matrix with its spectrum when its eigenvalues are integers and provided tight bounds on the size of the largest element of the SNF when the matrix is diagonalizable with nonzero integer eigen values.
17 citations