Problem:
Find the $\ell_2$ norm of the following vector:
$\left(
\begin{array}{c}
 -8 \\
 6 \\
 5 \\
 -1 \\
 2 \\
 -8 \\
 1 \\
 -1 \\
\end{array}
\right)$.
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Find the norm of the vector }\, (-8,6,5,-1,2,-8,1,-1)\, : \\
 \| \, (-8,6,5,-1,2,-8,1,-1)\, \|  \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{The }\text{formula }\text{for }\text{the }\text{8-dimensional }\text{Euclidean }\text{norm }\text{comes }\text{from }\text{the }\text{8-dimensional }\text{Pythagorean }\text{theorem}: \\
 \left\| \, \left(v_1,v_2,v_3,v_4,v_5,v_6,v_7,v_8\right)\, \right\| =\sqrt{v_1^2+v_2^2+v_3^2+v_4^2+v_5^2+v_6^2+v_7^2+v_8^2} \\
\end{array}
 \\
 
\begin{array}{l}
 \text{Substitute }\, (-8,6,5,-1,2,-8,1,-1)\,  \text{into }\text{the }\text{formula}: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & \| \, (-8,6,5,-1,2,-8,1,-1)\, \| =\sqrt{(-8)^2+6^2+5^2+(-1)^2+2^2+(-8)^2+1^2+(-1)^2}=14 \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/linear_algebra/lp_norm_w_steps/922.txt'}