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, bounds on the absolute values of the left and right eigenvalues of quaternionic matrix polynomials are devised and illustrated for the matrix p norm, where p = 1, 2, \infty, F.
Abstract: Localization theorems are discussed for the left and right eigenvalues of block quaternionic matrices. Basic definitions of the left and right eigenvalues of quaternionic matrices are extended to quaternionic matrix polynomials. Furthermore, bounds on the absolute values of the left and right eigenvalues of quaternionic matrix polynomials are devised and illustrated for the matrix p norm, where \({p = 1, 2, \infty, F}\). The above generalizes the bounds on the absolute values of the eigenvalues of complex matrix polynomials, which give sharper bounds to the bounds developed in [LAA, 358, pp. 5–22 2003] for the case of 1, 2, and \({\infty}\) matrix norms.
6 citations
TL;DR: In this article, two theorems on singular values and eigenvalues are given. But they do not consider singular value and Eigenvalue singularity in the same model.
Abstract: (1990). Two Theorems on Singular Values and Eigenvalues. The American Mathematical Monthly: Vol. 97, No. 1, pp. 47-50.
6 citations
TL;DR: For general n, the problem of determining the maximum value of the permanent over n-by-n real symmetric positive semidefinite matrices with given eigenvalues λ 1, λ 2, λ 3 has been studied in this paper.
Abstract: For general n the problem of determining the maximum value of the permanent over n-by-n real symmetric positive semidefinite matrices with given eigenvalues λ1,…,λn remains open. For n = 3 we present a solution and note that there is always a persymmetric maximizing matrix. Unfortunately, the solution is rather complicated; the maximum is always of the form for some ordering of the eigenvalues.
6 citations
01 Sep 2006
TL;DR: In this paper, the authors presented the characterization of the discrete-time fractional Brownian motion (dfBm) and observed that the eigenvalues of the auto-covariance matrix of a dfBm are dependent on the Hurst exponent characterizing this process.
Abstract: In this paper, we present the characterization of the discrete-time fractional Brownian motion (dfBm). Since, these processes are non-stationary; the auto-covariance matrix is a function of time. It is observed that the eigenvalues of the auto-covariance matrix of a dfBm are dependent on the Hurst exponent characterizing this process. Only one eigenvalue of this auto-covariance matrix depends on time index n and it increases as the time index of the auto-covariance matrix increases. All other eigenvalues are observed to be invariant with time index n in an asymptotic sense. The eigenvectors associated with these eigenvalues also have a fixed structure and represent different frequency channels. The eigenvector associated with the time-varying eigenvalue is a low pass filter
6 citations
TL;DR: In this paper, an upper limit for the number of intersections is derived in terms of the rank of the Gramian of the symmetrized products of order 0, 1, …, n − 1 of A and B.
6 citations