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Volume 16, Issue 2
On Matrix Unitarily Invariant Norm Condition Number

Daosheng Zhang

J. Comp. Math., 16 (1998), pp. 121-128.

Published online: 1998-04

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  • Abstract

In this paper, the unitarily invariant norm $\|\cdot\|$ on $\mathbb{C}^{m\times n}$ is used. We first discuss the problem under what case, a rectangular matrix $A$ has minimum condition number $K (A)=\| A \| \ \|A^+\|$, where $A^+$ designates the Moore-Penrose inverse of $A$; and under what condition, a square matrix $A$ has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of $K (A)=\|A\| \ \|A^{-1}\|_2$ in error estimation. 

  • Keywords

Matrix, unitarily invariant norm, condition number.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-16-121, author = {Zhang , Daosheng}, title = {On Matrix Unitarily Invariant Norm Condition Number}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {2}, pages = {121--128}, abstract = {

In this paper, the unitarily invariant norm $\|\cdot\|$ on $\mathbb{C}^{m\times n}$ is used. We first discuss the problem under what case, a rectangular matrix $A$ has minimum condition number $K (A)=\| A \| \ \|A^+\|$, where $A^+$ designates the Moore-Penrose inverse of $A$; and under what condition, a square matrix $A$ has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of $K (A)=\|A\| \ \|A^{-1}\|_2$ in error estimation. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9146.html} }
TY - JOUR T1 - On Matrix Unitarily Invariant Norm Condition Number AU - Zhang , Daosheng JO - Journal of Computational Mathematics VL - 2 SP - 121 EP - 128 PY - 1998 DA - 1998/04 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9146.html KW - Matrix, unitarily invariant norm, condition number. AB -

In this paper, the unitarily invariant norm $\|\cdot\|$ on $\mathbb{C}^{m\times n}$ is used. We first discuss the problem under what case, a rectangular matrix $A$ has minimum condition number $K (A)=\| A \| \ \|A^+\|$, where $A^+$ designates the Moore-Penrose inverse of $A$; and under what condition, a square matrix $A$ has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of $K (A)=\|A\| \ \|A^{-1}\|_2$ in error estimation. 

Zhang , Daosheng. (1998). On Matrix Unitarily Invariant Norm Condition Number. Journal of Computational Mathematics. 16 (2). 121-128. doi:
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