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Topic: Inequalities in matrices
Replies: 8   Last Post: Apr 23, 2013 5:04 PM

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Posts: 12,067
Registered: 7/15/05
Re: Inequalities in matrices
Posted: Apr 23, 2013 12:53 PM
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dullrich wrote:
>quasi wrote:
>> 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
> <(A-B) x, x> > 0
>for all x <> 0.



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