Modulus of continuity of the matrix absolute value |
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| Authors: | Rajendra Bhatia |
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| Affiliation: | 1.Indian Statistical Institute,New Delhi,India |
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| Abstract: | Lipschitz continuity of the matrix absolute value |A| = (A*A)1/2 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 | $
left| { left| A right| - left| B right| } right| leqslant left( {1 + log M_1 M_2 } right) left| {A - B} right|
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left| { left| A right| - left| B right| } right| leqslant left( {1 + log M_1 M_2 } right) left| {A - B} right|
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