quasi
Posts:
10,476
Registered:
7/15/05


Re: Inequalities in matrices
Posted:
Apr 23, 2013 12:53 PM


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.
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

