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

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Posts: 137
Registered: 3/4/09
Re: Inequalities in matrices
Posted: Apr 23, 2013 5:04 PM
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On Tue, 23 Apr 2013 12:15:06 -0500, wrote:

>On Tue, 23 Apr 2013 12:38:24 -0500, quasi <quasi@null.set> wrote:

>>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.

>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)

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