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Advanced/Introduction to Quantum/parts/00 vectors.tex
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@ -8,9 +8,9 @@ For example, $\left[\begin{smallmatrix} 1 \\ 3 \\ 2 \end{smallmatrix}\right]$ is
\definition{Euclidean norm} \definition{Euclidean norm}
The length of an $n$-dimensional vector $v$ is computed as follows: The length of an $n$-dimensional vector $v$ is computed as follows:
\begin{equation*} \begin{equation*}
|v| = \sqrt{v_0^2 +v_1^2 + ... + v_n^2} |v| = \sqrt{v_1^2 + ... + v_n^2}
\end{equation*} \end{equation*}
Where $v_0$ through $v_n$ represent individual components of this vector. For example, Where $v_1$ through $v_n$ represent individual components of this vector. For example,
\begin{equation*} \begin{equation*}
\left|\left[\begin{smallmatrix} 1 \\ 3 \\ 2 \end{smallmatrix}\right]\right| = \sqrt{1^2 + 3^2 + 2^2} = \sqrt{14} \left|\left[\begin{smallmatrix} 1 \\ 3 \\ 2 \end{smallmatrix}\right]\right| = \sqrt{1^2 + 3^2 + 2^2} = \sqrt{14}
\end{equation*} \end{equation*}