Does anyone know who coined the term orthonormal to refer to a basis that is orthogonal and normal.
In such a poorly named mathematical world (looking at you conditionally convergent series) I think we should shine more light on good naming, such as orthonormal. Some may argue that it can be confused with orthogonal, but to that I say just be better. Its concise, it sounds nice, and it is very very intuitive.
So if anyone knows the mathematician who popularized the term I would be forever greatful, all you get when you look it up is the Gram-Schmidt process (no disrespect to my boys Gram and Schmidt tho, they're G's fr)
Thank you
The earliest attestation I've found so far (not a coinage) is in Salomon Bochner, "Additive set functions on groups", Annals of Mathematics, Oct., 1939, Second Series, Vol. 40, No. 4 (Oct., 1939), pp. 769-799. Bochner uses the word "orthonormal" seven times, without defining it, which means that the editor and intended readers were already familiar with it. The first usage is, "Let $C$ be an arbitrary module and $\{ \varphi_{\alpha}(x) \}$ an arbitrary (not necessarily countable) orthonormal system of elements from $C$ [12]." Reference 12 is a 1936 paper of van Kampen that does not contain the word "orthonormal". If I had to guess, I'd guess that the term was perhaps used informally throughout the mid-1930s, too informal in '36 for van Kampen to use it, but respectable by '39. That might be way off, though.