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

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David C. Ullrich

Posts: 3,517
Registered: 12/13/04
Re: Inequalities in matrices
Posted: Apr 23, 2013 1:15 PM
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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
>> <(A-B) x, x> > 0
>>for all x <> 0.


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