AP
Posts:
137
Registered:
3/4/09


Re: Inequalities in matrices
Posted:
Apr 23, 2013 5:04 PM


On Tue, 23 Apr 2013 12:15:06 0500, dullrich@sprynet.com wrote:
>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? > >> Th of Perron if A>0 ( for all i,j a_i,j (real) >0) then A has an eigenvalue r>0 and there exist U>0 such as AU=rU ( all u_i >0)

