The indication is: Let $P$ is a symmetric positive definite matrix such that the norm of $p^k$ is smaller than a constant $C$ for every integer $k$, then $P=I_n$.
Prove that $O(n)$ is a maximal compact subgroup of $GL(n,\mathbb R)$
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4Does the title and the question have anything to do with each other? What is the question? – 2012-09-26
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0@DavideGiraudo You $P$ has $P^{-k} = 2^k I_n$ which has unbounded norms. – 2012-09-26
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0Sorry I realize that integer means positive and negative integers. – 2012-09-26