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Jun 21, 2011 at 0:19 comment added Suvrit Given the relation to $1/z$, it seems that for being viewed as a matrix function, the Drazin inverse seems to be the correct object. I did not previously know of this nice relation.
Jun 20, 2011 at 23:36 vote accept Glynne
Jun 20, 2011 at 23:36 comment added Glynne Thanks. The relationship does not hold (in general) for either the Moore-Penrose inverse or the regular matrix inverse. I assume that's because of those $zero$ eigenvalues?
Jun 19, 2011 at 1:35 history answered Suvrit CC BY-SA 3.0