
Re: Inequalities in matrices
Posted:
Apr 23, 2013 1:15 PM


On Tue, 23 Apr 2013 12:38:24 0500, quasi <quasi@null.set> wrote:
>dullrich wrote: >>quasi wrote: >>>gyansorova@gmail.com wrote: >>> >>>>If I have >>>> >>>>A>B where A and B are the same type of matrices  >>>>what does this mean? >>> >>>It usually means A[i,j] > B[i,j] for all i,j. >> >>Reasonable guess. But you shouldn't post guesses as though >>they were facts. > >Well, there are quite a few books on nonnegative matrices, >and all of them use the notation > > A >= 0 > >to mean > > A[i,j] >= 0 for all i,j, > >so that was from memory, not a guess.
Really? That seems very curious. What's an example of such a book?
> >But now that I've checked one of them, it's clear that those >books don't extend the notation A >= 0 to the notation A >= B, >so for that, I stand corrected. > >>What it really means is that A  B is positive definite. >>Which means that >> >> <(AB) x, x> > 0 >> >>for all x <> 0. > >Ok. > >quasi

