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#1 2012-11-20 20:00:09

princess snowwhite
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matrix

let P be any n*n square matrix whose row sum equals 1 then for any postive m the row sum of the matrix P^m equals 1 ,state true or false

#2 2012-11-20 20:57:13

bobbym
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Re: matrix

Hi princess snowwhite;

I am not sure about the term row sum. If you mean that each row sums to 1 then the matrix is called stochastic and is used in Markov processes. Every integer power of that matrix will also be stochastic meaning the rows sum to 1. So, I would say yes.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-11-20 20:58:48

princess snowwhite
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Re: matrix

Yes It Does Mean That Each Roq Sums To 1

#4 2012-11-20 21:03:55

bobbym
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Re: matrix

Then I would say the answer is yes but I do not remember how to prove that.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2012-11-20 21:09:00

bob bundy
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Re: matrix

hi princess snowwhite

Just proved it is true for all 2 x 2 matrices (algebraically).  Don't think I can generalise that method of proof though.  sad

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#6 2012-11-20 21:17:32

bob bundy
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Re: matrix

Just gone a step further, which may then lead to an inductive proof.

If A and B are 2 x 2 matrices having the property, the AB has the property.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#7 2012-11-21 00:59:20

bob bundy
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Re: matrix

I think I can put together a proof for n x n if you wish.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#8 2012-11-21 01:02:49

anonimnystefy
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Re: matrix

Hi Bob

How would you do an iinductive proof here?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#9 2012-11-21 02:44:26

bob bundy
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Re: matrix

Good question.  I abandoned that idea and went for a aij type proof instead.  It's just in my head so who knows how it will look when it goes down in type.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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