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Suppose we have a Matrix N, what does it mean if $N^T \cdot N =1$? My Thought was that either they are orthogonal or perhaps that N is orthogonal and hence $N^T=N^{-1}$ so we get $N^T N=N^{-1}N=I$ because if we multiply $ N^T \cdot N=1$ by I we get $ N^T \cdot N \cdot I=1 \cdot I=NN^T=I$.

Note that "I" here of course is the identity matrix. Is this reasoning okay?

Thanks in advance!

Randy
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    Yes we are dealing with orthogonal matrix! Look at https://math.stackexchange.com/q/768098/867100 – Nik Feb 26 '21 at 09:13
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    If $1$ means the real number $1$, the equality means that $N$ is a unit vector. – user1551 Feb 26 '21 at 10:10

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