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Mar 17 at 13:15 history edited Iosif Pinelis CC BY-SA 4.0
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Mar 15 at 2:13 comment added Iosif Pinelis @KatsanikJr : Yes, indeed. On the other hand, as shown by Christian Remling, this condition cannot be dropped.
Mar 14 at 10:23 comment added KatsanikJr @IosifPinelis Thank you for the clarification Prof. Pinelis. So considering that the \| AB\|\le \|A\|\, \|B\| property holds only then this proof is strong . Am I correct ?
Mar 12 at 17:36 comment added Iosif Pinelis @ChristianRemling : Thank you for your comments. Indeed, I thought this could only be true for operator matrix norms -- as your example now shows.
Mar 12 at 14:48 comment added Christian Remling And the source mentioned by the OP does refer to this site: en.wikipedia.org/wiki/Matrix_exponential#The_exponential_map
Mar 12 at 14:36 comment added Christian Remling At least according to the usage suggested here, a "matrix norm" is just a norm on the vector space of matrices; it need not satisfy $\| AB\|\le \|A\|\, \|B\|$: en.wikipedia.org/wiki/Matrix_norm
Mar 12 at 12:28 history answered Iosif Pinelis CC BY-SA 4.0