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On the construction of p-eigenvectors
Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, 2020Summary: Recent investigations led to the definition of \(p\)-eigenvectors: such vectors for a matrix, that the fraction of the vector norms of the matrix-vector product and the nonzero vector (as in defining a natural matrix norm) is independent of the applied \(p\)-norm. This paper elaborates this concept further, presenting general results, proof of
Lócsi, Levente, Németh, Zsolt
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2007
Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space.
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Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space.
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An improved eigenvector beamformer
ICASSP '84. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005Most techniques for computing beamformer tap weights do so by maximizing the overall signal-to-noise ratio at the system output, where noise includes both thermal noise and directional interference. This is the optimal solution if the two noise sources count equally.
Todd K. Citron, Thomas Kailath
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Eigenvectors of a Raman Medium
Physical Review Letters, 2000We show the existence of discrete sets of Raman sidebands which self-consistently establish a Raman coherence and propagate without change in amplitude and relative phase. Equivalently, there exist periodic femtosecond-time-scale, temporal pulse shapes which propagate without change in shape.
, Yavuz, , Sokolov, , Harris
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ON RIGHT AND LEFT EIGENVECTORS
JP Journal of Algebra, Number Theory and Applications, 2019Summary: In this paper, we show that if \(\lambda\) is an eigenvalue of a square matrix \(\mathcal{A}\), then by using the largest non-singular sub-matrix of the matrix \(\mathcal{A}_\lambda=\mathcal{A}-\lambda\mathcal{I}\), we may obtain all the linearly independent right and left eigenvectors of \(\mathcal{A}\), corresponding to the eigenvalue ...
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Derivatives and Perturbations of Eigenvectors
SIAM Journal on Numerical Analysis, 1988Es sei \(D\subset {\mathbb{C}}\) ein Gebiet, A(z) sei eine \(n\times n\)-Matrix, deren Elemente auf D definierte Funktionen von z sind, und x(z), y(z) seien n-dimensionale Vektorfelder auf D, wobei x(z) speziell Eigenvektor von A(z) zum Eigenwert \(\lambda\) (z) sei. Schließlich bedeute \(\sigma\) : \({\mathbb{C}}^ n\times {\mathbb{C}}^ n\to {\mathbb{C}
Meyer, Carl D., Stewart, G. W.
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An eigenvector variability plot
2009Summary: Principal components analysis is perhaps the most widely used method for exploring multivariate data. We propose a variability plot composed of measures on the stability of each eigenvector over samples as a data exploration tool. We also show that this variability measure gives a good measure on the intersample variability of eigenvectors ...
Tu, I. P., Chen, H., Chen, X.
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Communications of the ACM, 1963
M. L. Pei [ Comm. ACM 5 , 10 (Oct. 1962)] gave an explicit inverse for a matrix of the form M + δI , where M is an n -square matrix of ones and δ is a nonzero parameter.
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M. L. Pei [ Comm. ACM 5 , 10 (Oct. 1962)] gave an explicit inverse for a matrix of the form M + δI , where M is an n -square matrix of ones and δ is a nonzero parameter.
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