Showing papers on "Spectrum of a matrix published in 1967"
TL;DR: In this article, the authors considered both for hermitian and non-hermitian A. The properties are important in connexion with several algorithms for diagonalizing matrices by similarity transformations.
49 citations
07 Apr 1967
TL;DR: In this paper, the spectral density matrix of a zero-mean multiple stationary time series is defined and principal component theory is used to investigate the eigenvalues of a sample spectral density matrices.
Abstract: : This report describes some interpretations and uses of eigenvalues and eigenvectors of spectral and sample spectral density matrices of multiple stationary time series. The spectral density matrix of a zero-mean multiple stationary time series is defined. Eigenvalues and eigenvectors of the spectral density matrix are discussed and principal component theory is presented. Statistical distribution theory and related results are used to investigate the eigenvalues of a sample spectral density matrix. This investigation gives methods for obtaining simultaneous confidence bounds on the elements of the true spectral density matrix and its inverse, and also methods for obtaining confidence bounds on the eigenvalues of the true spectral density matrix.
5 citations
TL;DR: If A is a completely continuous self-adjoint operator on a Hilbert space its eigenvalues are the values of the inner product at stationary points on the unit sphere provided that certain regularity conditions hold at the eigenvectors.
3 citations
TL;DR: In this paper, the stability of a large sampled system is examined by finding the eigenvalues of the difference equation that describes the system, and the derivatives of these eigen values with respect to the system parameters are found to give the sensitivity of the system to the various parameters.
Abstract: The stability of a large sampled system is examined by finding the eigenvalues of the difference equation that describes the system. The derivatives of these eigenvalues with respect to the system parameters are found to give the sensitivity of the system to the various parameters. A method of finding the difference equations for the system is described which is based on exponentiating the matrix of the system with the samplers open. The problem of multiple eigenvalues is considered, and a block-form solution is used to determine the nature of the multiplicity of the multiple eigenvalues.
3 citations
3 citations
1 citations