[Analysis] Diff. Calc.

semester3/analysis-ii/cheat-sheet-rb/parts/01_linalg.tex

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+Relevant definitions used throughout Analysis II.
+
+\definition \textbf{Euclidian Norm} $||x|| := \displaystyle\sqrt{\sum_{i=1}^{n} x_i^2}$\\
+\subtext{Used to generalize $|x|$ in many Analysis I definitions}
+
+\lemma \textbf{Properties of} $||x||$
+\begin{center}
+    $
+    \begin{array}{ll}
+        (i)     & ||x|| \geq 0 \\
+        (ii)    & ||x|| \iff x = 0 \\
+        (iii)   & ||\alpha x|| = \alpha \cdot ||x|| \\
+        (iv)    & ||x + y|| \leq ||x|| + ||y||\quad \text{(Triangle Inequality)}
+    \end{array}
+    $
+\end{center}
+\subtext{$\forall x,y \in \R^n,\quad \alpha \in \R\\$}