A matrix with real entries and orthonormal columns preserves dot products.

Created almost 9 years ago, updated about 8 hours ago

If real $Q^TQ=I$, then $\langle Qx,Qy\rangle=x^TQ^TQy=x^Ty=\langle x,y\rangle$. Thus dot products and angles are preserved. The complex analogue uses $Q^*Q=I$ and preserves the Hermitian inner product.

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