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After my question whose answer turned out to be false, I re-examined the course of my proof, which is actually seperate from the one in my question, and found out that there's another condition, at ...

I was working more on the topic on my previous question when I have to know whether the following statement is true to circumvent the "exception" caused by division by singular matrices; ...

Let $S$ be the set of real matrices with at least one real logarithm. For some couple of its elements, for example those with at least (one real logarithm each with submultiplicative norm smaller than ...