[Analysis] Diff. Calc.

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

@@ -19,4 +19,15 @@ Relevant definitions used throughout Analysis II.
     $
 \end{center}
 
+\definition \textbf{Definiteness}
+\begin{center}
+    $
+    \begin{array}{lcl}
+        \text{Positive Definite} &\iffdef& x^\top \textbf{A} x > 0\ \forall x \in \R^n_{\neq 0} \\
+        \text{Negative Definite} &\iffdef& x^\top \textbf{A} x < 0\ \forall x \in \R^n_{\neq 0}
+    \end{array}
+    $
+\end{center}
+\smalltext{If $0$ is allowed, $\textbf{A}$ is called positive/negative semi-definite.}
+
 \definition \textbf{Trace} $\text{Tr}(\textbf{A}) := \displaystyle\sum_{i=0}^{\text{min}(m,n)} \textbf{A}_{i, i}$