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Assume that $V$ is a finite dimensional vector space over $\mathbb{R}$ with two bases $\alpha$ and $\beta$. What are the necessary and/or sufficient conditions for the basis transformation matrix from $\alpha$ to $\beta$ (transition matrix) to be orthogonal?

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closed as off-topic by Jack, Davide Giraudo, suomynonA, Behrouz Maleki, user91500 Dec 14 '16 at 5:45

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  • $\begingroup$ If $\alpha$ is an orthonormal basis, then it is necessary and sufficient that $\beta$ should also be orthonormal. $\endgroup$ – Omnomnomnom Dec 13 '16 at 20:45

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