The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns
ID: the-orthogonal-group-is-the-group-of-all-matrices-with-orthonormal-rows-and-orthonormal-columns
The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns by 
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01Or 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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