One encounters often in numerics non-square matrices with orthonormal columns, i.e., $U\in\mathbb{R}^{m\times n}$, with $m > n$, such that $U^TU=I$ (but, clearly, $UU^T \neq I$).


Is there a name for these matrices?



Is there a standard name for (non-square) matrices with orthonormal columns?
***Orthonormal $\boldsymbol n$-frames*** :  <https://en.wikipedia.org/wiki/Stiefel_manifold>.


Added: This terminology of Hirzebruch ([1966](//ams.org/mathscinet-getitem?mr=202713)), Steenrod ([1951](//ams.org/mathscinet-getitem?mr=39258)) translates the ***$\boldsymbol n$-Systeme*** of Stiefel ([1936](//zbmath.org/?q=an:0014.41601)), ***$\boldsymbol n$-podes***, ***$\boldsymbol n$-pèdes*** or ***multipèdes*** of Einstein ([1931](//zbmath.org/?q=an:57.1199.04)), Waelsch ([1907](//zbmath.org/?q=an:38.0482.01)), ***$\boldsymbol n$-Beine*** or ***Vielbeine*** of Hirzebruch ([1956](//ams.org/mathscinet-getitem?mr=82174)), [Einstein](http://echo.mpiwg-berlin.mpg.de/MPIWG:YP5DFQU1) ([1928](//zbmath.org/?q=an:54.0942.04)), Blaschke ([1920](https://zbmath.org/?q=an:47.0694.02)), or [Waelsch](//books.google.com/books?id=lqEKAAAAYAAJ&pg=PA246&dq=Vielbein+bein) ([1906](//zbmath.org/?q=an:37.0113.01)).


