What's the history of the development of the notation for (real or hermitian) scalar product? In particular,


Did "bra-ket" notations, such as $\langle u\mid v\rangle$ or $(u\mid v)$, first arise with Paul Dirac in the context of quantum mechanics?


Did the $\langle u, v\rangle$ notation appear later as a modification of the one with the vertical bar or vice versa?


Was the "dot product" notation $\overrightarrow{u}\bullet\overrightarrow{u}$ introduced before the "bra-ket" ones?



History of the notation for scalar product
Cajori, *A History of Mathematical Notation* § 506 (vol 2) attributes to Grassmann the notations $a \times b$ (1848) and $[a|b]$ (1862) for the scalar product, to Heaviside and others the $a|b$ in the 1890s, to Lorentz $(a,b)$ in the early 1900s.


