July 10th, 2011, 03:32 PM  #1 
Member Joined: May 2011 Posts: 38 Thanks: 0  diagonal matrix
let A b a 2x2 diagonal matrix with real values a11 and a22 along the diagonal. show that for every positive integer n, A^n is a diagonal matrix whose diagonal elements are a11^n and a22^n

July 10th, 2011, 03:48 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: diagonal matrix
Use mathematical induction. Look at AČ, and then show that if the kth power is diagonal in the way described, so is the (k+1)th. By the way, when you start a new thread on a problem, always please show as much as possible of what you have tried so far. 
July 11th, 2011, 12:12 PM  #3 
Senior Member Joined: Jan 2011 Posts: 106 Thanks: 0  Re: diagonal matrix
As far as I am concerned, this holds for diagonal matrices of ANY order!


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