Magnitude Where nnn is the dimensions, the magnitude of ∣ψ⟩\left\lvert \psi \right\rangle∣ψ⟩ is defined as: ∣∣∣ψ⟩∣∣=∣∣(ψ1ψ2⋮ψn)∣∣=∣ψ1∣2+∣ψ2∣2+...+∣ψn∣2\begin{gather*} ||\left\lvert \psi \right\rangle||=||\begin{pmatrix}\psi_1\\\psi_2\\\vdots\\\psi_n\end{pmatrix}||=\sqrt{|\psi_1|^2+|\psi_2|^2+...+|\psi_n|^2} \end{gather*}∣∣∣ψ⟩∣∣=∣∣ψ1ψ2⋮ψn∣∣=∣ψ1∣2+∣ψ2∣2+...+∣ψn∣2 Note that ∣∣∣ψ⟩∣∣2=⟨ψ∣ψ⟩||\left\lvert \psi \right\rangle||^2=\left\langle \psi|\psi \right\rangle∣∣∣ψ⟩∣∣2=⟨ψ∣ψ⟩ You’ll know what a bra-ket is later.Matrix Multiplication