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e-i-i-N-e-i-is-a-basis-vector-A-C-n-A-i-N-e-i-A-i-A-1-A-2-A-n-A-B-B-T-A-B-




Question Number 11217 by FilupS last updated on 17/Mar/17
∃e_i :i∈N        e_i  is a basis vector  A∈C^n   A=Σ_(i∈N) e_i A_i = ((A_1 ),(A_2 ),(⋮),(A_n ) )   = ∣A⟩  ⟨B∣=(∣B^∗ ⟩)^T   ∣A⟩⟨B∣=???
$$\exists{e}_{{i}} :{i}\in\mathbb{N}\:\:\:\:\:\:\:\:{e}_{{i}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{vector} \\ $$$$\boldsymbol{{A}}\in\mathbb{C}^{{n}} \\ $$$$\boldsymbol{{A}}=\underset{{i}\in\mathbb{N}} {\sum}{e}_{{i}} {A}_{{i}} =\begin{pmatrix}{{A}_{\mathrm{1}} }\\{{A}_{\mathrm{2}} }\\{\vdots}\\{{A}_{{n}} }\end{pmatrix}\:\:\:=\:\mid{A}\rangle \\ $$$$\langle{B}\mid=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}} \\ $$$$\mid{A}\rangle\langle{B}\mid=??? \\ $$

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