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July 10th, 2011, 03:32 PM   #1
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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
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July 10th, 2011, 03:48 PM   #2
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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.
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July 11th, 2011, 12:12 PM   #3
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Re: diagonal matrix

As far as I am concerned, this holds for diagonal matrices of ANY order!
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