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 |
|---|---|
| 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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