Fix typos in PCA lecture

Author: gpleiss

_freeze/schedule/lectures/lecture_13_pca/execute-results/html.json

@@ -104,7 +104,7 @@ we saw that not all high dimensional data was doomed to fail with kNN or kernel
 
 - We can now represent our data in this new rotated space via
 
-  $$ \boldsymbol Z = [\boldsymbol V]_{:,1:k} = \boldsymbol X \boldsymbol Q, $$
+  $$ \boldsymbol Z = \boldsymbol X [\boldsymbol V]_{:,1:k} = \boldsymbol X \boldsymbol Q, $$
 
 - We refer to the new features in $\boldsymbol Z$ as the **principal components** (PCs) of the data.
 
@@ -222,10 +222,10 @@ popmusic_train
 
   $$
     \underbrace{\boldsymbol X}_{n \times 2} \: \longrightarrow \: \underbrace{\boldsymbol \Phi}_{n \times 14} = \begin{bmatrix}
-    1 & X_{11} & X_{12} & X_{11}^2 & X_{11} X_{12} & X_{12}^2 & \ldots & X_{12}^4 \\
-    1 & X_{21} & X_{22} & X_{21}^2 & X_{21} X_{22} & X_{22}^2 & \ldots & X_{22}^4 \\
+    X_{11} & X_{12} & X_{11}^2 & X_{11} X_{12} & X_{12}^2 & \ldots & X_{12}^4 \\
+    X_{21} & X_{22} & X_{21}^2 & X_{21} X_{22} & X_{22}^2 & \ldots & X_{22}^4 \\
     \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\
-    1 & X_{n1} & X_{n2} & X_{n1}^2 & X_{n1} X_{n2} & X_{n2}^2 & \ldots & X_{n2}^4
+    X_{n1} & X_{n2} & X_{n1}^2 & X_{n1} X_{n2} & X_{n2}^2 & \ldots & X_{n2}^4
     \end{bmatrix}
   $$