[latexpage]

The ket 

The ket is short-hand for a column vector

\[

[+preamble]
\newcommand{\braket}[2]{\left\langle{#1} \, \middle|\, {#2}\right\rangle}
\newcommand{\ket}[1]{\left|\,{#1} \right\rangle}
\newcommand{\bra}[1]{\left\langle{#1} \, \right |}
[/preamble]

\ket{a} = \begin{bmatrix}
a_1 \\
a_2 \\
\vdots \\
a_N
\end{bmatrix} \\

\]

The ket $\ket{a} $ and the vector a represent the same vector in the V space; i.e., $a \in V$ and $\ket{a} \, \,\in V$

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