Modulus of continuity of the matrix absolute value

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| = (AA) 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
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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