Question Number 11217 by FilupS last updated on 17/Mar/17
$$\exists{e}_{{i}} :{i}\in\mathbb{N}\:\:\:\:\:\:\:\:{e}_{{i}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{vector} \\ $$$$\boldsymbol{{A}}\in\mathbb{C}^{{n}} \\ $$$$\boldsymbol{{A}}=\underset{{i}\in\mathbb{N}} {\sum}{e}_{{i}} {A}_{{i}} =\begin{pmatrix}{{A}_{\mathrm{1}} }\\{{A}_{\mathrm{2}} }\\{\vdots}\\{{A}_{{n}} }\end{pmatrix}\:\:\:=\:\mid{A}\rangle \\ $$$$\langle{B}\mid=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}} \\ $$$$\mid{A}\rangle\langle{B}\mid=??? \\ $$