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#1 2012-11-20 20:00:09
- princess snowwhite
- Member
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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
- Administrator
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2012-11-20 21:03:55
- bobbym
- Administrator
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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#8 2012-11-21 01:02:49
- anonimnystefy
- Real Member
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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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#9 2012-11-21 02:44:26
- bob bundy
- Moderator
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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