Update analysis_ii.tex

Author: samwatt6

IB_M/analysis_ii.tex

@@ -3047,7 +3047,7 @@ \subsection{Inverse function theorem}
   \begin{align*}
     \|A \mathbf{x}\|^2 &= \sum_{i = 1}^m \left(\sum_{j = 1}^n A_{ij} x_j\right)^2\\
     \intertext{By Cauchy-Schwarz, we have}
-    &\leq \sum_{i = 1}^m \left(\sum_{j = 1}^n a_{ij}^2\right)^2 \left(\sum_{j = 1}^n x_j^2\right)^2\\
+    &\leq \sum_{i = 1}^m \left(\sum_{j = 1}^n a_{ij}^2\right) \left(\sum_{j = 1}^n x_j^2\right)\\
     &= \|\mathbf{x}\|^2 \sum_{i = 1}^m \sum_{j = 1}^n a_{ij}^2.
   \end{align*}
   Dividing by $\|\mathbf{x}\|^2$, we know