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#1 2012-11-19 21:00:09
- princess snowwhite
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- Registered: 2012-11-06
- Posts: 29
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
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#2 2012-11-19 21:57:13
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2012-11-19 21:58:48
- princess snowwhite
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- Registered: 2012-11-06
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Re: matrix
Yes It Does Mean That Each Roq Sums To 1
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#4 2012-11-19 22:03:55
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2012-11-19 22:09:00
- Bob
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- Registered: 2010-06-20
- Posts: 10,621
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. 
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#6 2012-11-19 22:17:32
- Bob
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- Registered: 2010-06-20
- Posts: 10,621
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
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#7 2012-11-20 01:59:20
- Bob
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Re: matrix
I think I can put together a proof for n x n if you wish.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#8 2012-11-20 02:02:49
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: matrix
Hi Bob
How would you do an iinductive proof here?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
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#9 2012-11-20 03:44:26
- Bob
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- Registered: 2010-06-20
- Posts: 10,621
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
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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