Apparently this is simple, but I'm not seeing it. P, A are matrices, n is a real. Use induction to prove that . Presumably the first step is: I'm not sure what's next, or if that is correct.
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Originally Posted by scorpion007 Apparently this is simple, but I'm not seeing it. P, A are matrices, n is a real. Use induction to prove that . Presumably the first step is: I'm not sure what's next, or if that is correct. In brief: Step 1: True for n = 1. Step 2: Assume true for n = k. That is, assume is true. Step 3: Show true for n = k + 1. That is, assuming is true, show that . To do this, note that and substitute .
Last edited by mr fantastic; Mar 29th 2009 at 12:23 AM.
Originally Posted by mr fantastic In brief: Step 1: True for n = 1. Step 2: Assume true for n = k. That is, assume is true. Did you mean in the RHS?
Originally Posted by scorpion007 Did you mean in the RHS? Yes. I have made the necessary edit.
Thanks, I see it now: Expanding the last step would be: Correct? Too verbose?
Originally Posted by scorpion007 Thanks, I see it now: Expanding the last step would be: Correct? Too verbose? It's fine. Now you need to write out the complete proof by induction, dotting the i's and crossing the t's.
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