Volume 2, Issue 4
Bounds on Condition Number of a Matrix

Hong-Ci Huang

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J. Comp. Math., 2 (1984), pp. 356-360.

Published online: 1984-02

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  • Abstract

For each vetor norm ||x||, a matirx has its operator norm and a condition number. Let U be the set of the whole of norms defined on $C^n$. It is shown that for a nonsingular matrix $A\in C^{n\times n}$,there is no finite upper bound of p(A) whch ||.|| varies on U if $A\neq \alpha I$; on the other hand, it is shown that the if of A =$\ru(A)\ru(A^{-1}$ and in which case this infinum can or cannot be attained, where $\ru(A)$denotes the spectral radius of A.

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@Article{JCM-2-356, author = {Hong-Ci Huang}, title = {Bounds on Condition Number of a Matrix}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {4}, pages = {356--360}, abstract = { For each vetor norm ||x||, a matirx has its operator norm and a condition number. Let U be the set of the whole of norms defined on $C^n$. It is shown that for a nonsingular matrix $A\in C^{n\times n}$,there is no finite upper bound of p(A) whch ||.|| varies on U if $A\neq \alpha I$; on the other hand, it is shown that the if of A =$\ru(A)\ru(A^{-1}$ and in which case this infinum can or cannot be attained, where $\ru(A)$denotes the spectral radius of A. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9671.html} }
TY - JOUR T1 - Bounds on Condition Number of a Matrix AU - Hong-Ci Huang JO - Journal of Computational Mathematics VL - 4 SP - 356 EP - 360 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9671.html KW - AB - For each vetor norm ||x||, a matirx has its operator norm and a condition number. Let U be the set of the whole of norms defined on $C^n$. It is shown that for a nonsingular matrix $A\in C^{n\times n}$,there is no finite upper bound of p(A) whch ||.|| varies on U if $A\neq \alpha I$; on the other hand, it is shown that the if of A =$\ru(A)\ru(A^{-1}$ and in which case this infinum can or cannot be attained, where $\ru(A)$denotes the spectral radius of A.
Hong-Ci Huang. (1970). Bounds on Condition Number of a Matrix. Journal of Computational Mathematics. 2 (4). 356-360. doi:
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