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None element of orthogonal matrix can't have unit modulus larger then 1.

I've tried to use the properties of orthogonal matrices ( $|det(A)| = 1$ and $Q^T=Q^{-1}$ ) but I couldn't find out how they could help me.

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    $\begingroup$ Do you know that the columns of an orthogonal $n \times n$ matrix form a set of orthonormal vectors in $\mathbf{R}^{n}$ (or can you see how to deduce this easily from $Q^{T}Q = I$)...? $\endgroup$ – Andrew D. Hwang Jun 16 '17 at 17:11
  • $\begingroup$ @AndrewD.Hwang I know that,but how can that help me? $\endgroup$ – Dragan Zrilić Jun 16 '17 at 17:16
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    $\begingroup$ The magnitude squared of a vector is the sum of the squares of its components; for a unit vector, the magnitude squared is $1$. ;) $\endgroup$ – Andrew D. Hwang Jun 16 '17 at 18:07
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Note that $Q^T Q =1$. So, given $q_i$ the row $i$ of Q we have $q_i^Tq_i=1$. In other words, for all k, $q_{ik}^2 \leq \sum q_{ij}^2 = 1$. It means that $|q_{ik}|\leq 1$.

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