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The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns

Ciro Santilli (@cirosantilli, 37) ... Geometry Differential geometry Lie group Important Lie group Orthogonal group Definition of the orthogonal group
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
Or equivalently, the set of rows is orthonormal, and so is the set of columns. TODO proof that it is equivalent to the orthogonal group is the group of all matrices that preserve the dot product.

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