If $H$ is a finite-dimensional [Hilbert] space, then every basis of $H$ is a Riesz basis.
I thought that in the context of Hilbert spaces the unqualified term "basis" is usually taken to mean "Hilbert basis" (i.e. orthonormal basis), not "Hamel basis" (i.e. basis in the linear-algebra sense), but under that interpretation the restriction to finite-dimensional spaces makes no sense, since every Hilbert basis is a Riesz basis (with constants $c=C=1$). Am I right in thinking that
- they mean a Hamel basis, and
- it would be preferable to disambiguate that statement by inserting "Hamel"?