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Volume 3, Issue 3
The Spectral Variation of Pencils of Matrices

L. Elsner & P. Lancaster

J. Comp. Math., 3 (1985), pp. 262-274.

Published online: 1985-03

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  • Abstract

Perturbation theorems for the spectrum of a regular matrix pencil $λA-B$ are given. As it may include points near or at infinity the Euclidean distance is not appropriate. We use the chordal metric and the distances. For those purpose we develop here an algebraic treatment of matrix pairs, with special reference to diagonable and definite pairs, using ideas from the theory of matrix polynomials.

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@Article{JCM-3-262, author = {Elsner , L. and Lancaster , P.}, title = {The Spectral Variation of Pencils of Matrices}, journal = {Journal of Computational Mathematics}, year = {1985}, volume = {3}, number = {3}, pages = {262--274}, abstract = {

Perturbation theorems for the spectrum of a regular matrix pencil $λA-B$ are given. As it may include points near or at infinity the Euclidean distance is not appropriate. We use the chordal metric and the distances. For those purpose we develop here an algebraic treatment of matrix pairs, with special reference to diagonable and definite pairs, using ideas from the theory of matrix polynomials.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9623.html} }
TY - JOUR T1 - The Spectral Variation of Pencils of Matrices AU - Elsner , L. AU - Lancaster , P. JO - Journal of Computational Mathematics VL - 3 SP - 262 EP - 274 PY - 1985 DA - 1985/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9623.html KW - AB -

Perturbation theorems for the spectrum of a regular matrix pencil $λA-B$ are given. As it may include points near or at infinity the Euclidean distance is not appropriate. We use the chordal metric and the distances. For those purpose we develop here an algebraic treatment of matrix pairs, with special reference to diagonable and definite pairs, using ideas from the theory of matrix polynomials.

Elsner , L. and Lancaster , P.. (1985). The Spectral Variation of Pencils of Matrices. Journal of Computational Mathematics. 3 (3). 262-274. doi:
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