Volume 3, Issue 1
Estimation of the Separation of Two Matrices (II)

J. Comp. Math., 3 (1985), pp. 19-26

Published online: 1985-03

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• Abstract

In this paper we give a lower bound of the separation $sep_F(A,B)$ of two diagonalizable matrices A and B. The key to finding the lower bound of $sep_F(A,B)$ is to find an upper bound for the condition number of a transformation matrix Q which transforms a diagonalizable matrix A to a diagonal form. The obtained lower bound of $sep_F(A,B)$ involves the eigenvalues of A and B as well as the departures form the normality $\delta_F(A)$ and $\delta_F(B)$

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@Article{JCM-3-19, author = {Ji-Guang Sun}, title = {Estimation of the Separation of Two Matrices (II)}, journal = {Journal of Computational Mathematics}, year = {1985}, volume = {3}, number = {1}, pages = {19--26}, abstract = { In this paper we give a lower bound of the separation $sep_F(A,B)$ of two diagonalizable matrices A and B. The key to finding the lower bound of $sep_F(A,B)$ is to find an upper bound for the condition number of a transformation matrix Q which transforms a diagonalizable matrix A to a diagonal form. The obtained lower bound of $sep_F(A,B)$ involves the eigenvalues of A and B as well as the departures form the normality $\delta_F(A)$ and $\delta_F(B)$ }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9603.html} }
TY - JOUR T1 - Estimation of the Separation of Two Matrices (II) AU - Ji-Guang Sun JO - Journal of Computational Mathematics VL - 1 SP - 19 EP - 26 PY - 1985 DA - 1985/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9603.html KW - AB - In this paper we give a lower bound of the separation $sep_F(A,B)$ of two diagonalizable matrices A and B. The key to finding the lower bound of $sep_F(A,B)$ is to find an upper bound for the condition number of a transformation matrix Q which transforms a diagonalizable matrix A to a diagonal form. The obtained lower bound of $sep_F(A,B)$ involves the eigenvalues of A and B as well as the departures form the normality $\delta_F(A)$ and $\delta_F(B)$