diff --git a/slides/ddasp_exercise_slides.tex b/slides/ddasp_exercise_slides.tex
index f2a82f6..97bed8b 100644
--- a/slides/ddasp_exercise_slides.tex
+++ b/slides/ddasp_exercise_slides.tex
@@ -2678,6 +2678,10 @@ \subsection{Exercise 07}
 
 \end{frame}
 
+\begin{frame}{Ex07: Audio Features}
+% empty slide for clever touch
+\end{frame}
+
 
 
 
@@ -2773,9 +2777,9 @@ \subsection{Exercise 08}
 
 Mapping
 
-$\bm{X}_r = \bm{V} \cdot \bm{\Sigma}^\mathrm{T} \bm{U}^\mathrm{T} = \bm{L} \cdot \bm{F}_r$
+$\bm{X}_r = \bm{X}_c^\mathrm{T} = \bm{V} \cdot \bm{\Sigma}^\mathrm{T} \bm{U}^\mathrm{T} = \bm{L} \cdot \bm{F}_r$
 
-$\bm{F}_r = \bm{L}^\mathrm{T} \bm{X}_r = \bm{V}^\mathrm{T} \bm{X}_r = \bm{\Sigma}^\mathrm{T} \bm{U}^\mathrm{T} = (\bm{\Sigma} \bm{U})^\mathrm{T}$
+$\bm{F}_r = \bm{L}^\mathrm{T} \bm{X}_r = \bm{V}^\mathrm{T} \bm{X}_r = \bm{\Sigma}^\mathrm{T} \bm{U}^\mathrm{T} = ( \bm{U} \bm{\Sigma})^\mathrm{T}$
 
 PC scores $\bm{F}_r =
 \begin{bmatrix}
@@ -2785,7 +2789,7 @@ \subsection{Exercise 08}
 - \bm{f}_F -
 \end{bmatrix}
 =
-(\bm{\Sigma} \bm{U})^\mathrm{T}$
+(\bm{U} \bm{\Sigma})^\mathrm{T}$
 
 PC loadings $\bm{L} = \bm{V} $