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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: 3,555
Registered: 12/13/04
Re: Inequalities in matrices
Posted: Apr 23, 2013 9:35 AM
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On Mon, 22 Apr 2013 23:37:22 -0500, quasi <quasi@null.set> wrote:

>On Mon, 22 Apr 2013 19:55:39 -0700 (PDT), 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.

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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