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Volume 1, Issue 1
Orthogonal Projections and the Perturbation of the Eigenvalues of Singular Pencils

Ji-Guang Sun

J. Comp. Math., 1 (1983), pp. 63-74.

Published online: 1983-01

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  • Abstract

In this paper we obtain a Hoffman-Wielandt type theorem and a Bauer-Fike type theorem for singular pencils of matrics. These results delineate the relations between the perturbation of the eigenvalues of a singular diagonalizable pencil $A-λB$ and the variation of the orthogonal projection onto the column space $\mathcal{R} \Bigg( \begin{matrix} A^H \\ B^H  \end{matrix} \Bigg)$.

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@Article{JCM-1-63, author = {Ji-Guang Sun}, title = {Orthogonal Projections and the Perturbation of the Eigenvalues of Singular Pencils}, journal = {Journal of Computational Mathematics}, year = {1983}, volume = {1}, number = {1}, pages = {63--74}, abstract = {

In this paper we obtain a Hoffman-Wielandt type theorem and a Bauer-Fike type theorem for singular pencils of matrics. These results delineate the relations between the perturbation of the eigenvalues of a singular diagonalizable pencil $A-λB$ and the variation of the orthogonal projection onto the column space $\mathcal{R} \Bigg( \begin{matrix} A^H \\ B^H  \end{matrix} \Bigg)$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9682.html} }
TY - JOUR T1 - Orthogonal Projections and the Perturbation of the Eigenvalues of Singular Pencils AU - Ji-Guang Sun JO - Journal of Computational Mathematics VL - 1 SP - 63 EP - 74 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9682.html KW - AB -

In this paper we obtain a Hoffman-Wielandt type theorem and a Bauer-Fike type theorem for singular pencils of matrics. These results delineate the relations between the perturbation of the eigenvalues of a singular diagonalizable pencil $A-λB$ and the variation of the orthogonal projection onto the column space $\mathcal{R} \Bigg( \begin{matrix} A^H \\ B^H  \end{matrix} \Bigg)$.

Ji-Guang Sun. (1983). Orthogonal Projections and the Perturbation of the Eigenvalues of Singular Pencils. Journal of Computational Mathematics. 1 (1). 63-74. doi:
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