quasi
Posts:
9,891
Registered:
7/15/05


Re: Inequalities in matrices
Posted:
Apr 23, 2013 3:57 PM


dullrich wrote: >quasi wrote: >>dullrich wrote: >>>quasi wrote: >>>>gyansorova 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?
Bapat & Raghavan Nonnegative Matrices and Applications CUP, 1997
Berman & Plemmons Nonnegative Matrices in the Mathematical Sciences AP, 1979
Minc Nonnegative Matrices Wiley, 1988
>>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

