Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2012-11-19 21:00:09

princess snowwhite
Member
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

Offline

#2 2012-11-19 21:57:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

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.

Offline

#3 2012-11-19 21:58:48

princess snowwhite
Member
Registered: 2012-11-06
Posts: 29

Re: matrix

Yes It Does Mean That Each Roq Sums To 1

Offline

#4 2012-11-19 22:03:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,779

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.

Offline

#5 2012-11-19 22:09:00

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,259

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

Offline

#6 2012-11-19 22:17:32

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,259

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

Offline

#7 2012-11-20 01:59:20

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,259

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

Offline

#8 2012-11-20 02:02:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

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

Offline

#9 2012-11-20 03:44:26

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,259

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

Offline

Board footer

Powered by FluxBB