Bhatia, Rajendra
(2010)
*Modulus of continuity of the matrix absolute value*
Indian Journal of Pure & Applied Mathematics, 41
(1).
pp. 99-111.
ISSN 0019-5588

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Official URL: http://www.springerlink.com/index/TGL5943V23786745...

Related URL: http://dx.doi.org/10.1007/s13226-010-0014-0

## Abstract

Lipschitz continuity of the matrix absolute value |A| = (A^{∗}A) ^{½ } is studied. Let A and B be invertible, and let
M_{ 1} = max(||A||, ||B||), M_{ 2 }= max(||A ^{-1}||, ||B ^{-1}||). Then it is shown that A proof is given for the
well-known theorem that there is a constant c(n) such that for any two n × n matrices A and B || |A| - |B||| ≤ c(n) ||A - B|| and the best
constant in this inequality is O(log n).

Item Type: | Article |
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Source: | Copyright of this article belongs to Indian National Science Academy. |

Keywords: | Matrix Absolute Value; Perturbation Bound; Commutator; Triangular Truncation; Schur Product |

ID Code: | 2531 |

Deposited On: | 08 Oct 2010 07:01 |

Last Modified: | 08 Oct 2010 07:01 |

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