diff --git a/.github/workflows/dynare-6.2-matlab-r2024b-macos.yml b/.github/workflows/dynare-6.2-matlab-r2024b-macos.yml
index a6eaeed..b6b9642 100644
--- a/.github/workflows/dynare-6.2-matlab-r2024b-macos.yml
+++ b/.github/workflows/dynare-6.2-matlab-r2024b-macos.yml
@@ -83,4 +83,16 @@ jobs:
             cd("progs/matlab");
             AR4LagSelection;
             portmanteauTest;
-            bootstrapCIAR1;
\ No newline at end of file
+            bootstrapCIAR1;
+
+      - name: Run week 6 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("Dynare-6.2-arm64/matlab");
+            cd("progs/matlab");
+            matrixAlgebraEigenvalues;
+            matrixAlgebraKroneckerFormula;
+            matrixAlgebraRotation;
+            matrixAlgebraCholesky;
+            matrixAlgebraLyapunovComparison;
\ No newline at end of file
diff --git a/.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml b/.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml
index c20ddfc..af24c09 100644
--- a/.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml
+++ b/.github/workflows/dynare-6.2-matlab-r2024b-ubuntu.yml
@@ -113,3 +113,15 @@ jobs:
             AR4LagSelection;
             portmanteauTest;
             bootstrapCIAR1;
+
+      - name: Run week 6 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("dynare/matlab");
+            cd("progs/matlab");
+            matrixAlgebraEigenvalues;
+            matrixAlgebraKroneckerFormula;
+            matrixAlgebraRotation;
+            matrixAlgebraCholesky;
+            matrixAlgebraLyapunovComparison;
\ No newline at end of file
diff --git a/.github/workflows/dynare-6.2-matlab-r2024b-windows.yml b/.github/workflows/dynare-6.2-matlab-r2024b-windows.yml
index a871543..7f27d15 100644
--- a/.github/workflows/dynare-6.2-matlab-r2024b-windows.yml
+++ b/.github/workflows/dynare-6.2-matlab-r2024b-windows.yml
@@ -75,3 +75,15 @@ jobs:
             AR4LagSelection;
             portmanteauTest;
             bootstrapCIAR1;
+
+      - name: Run week 6 codes
+        uses: matlab-actions/run-command@v2
+        with:
+          command: |
+            addpath("D:\hostedtoolcache\windows\dynare-6.0\matlab");
+            cd("progs/matlab");
+            matrixAlgebraEigenvalues;
+            matrixAlgebraKroneckerFormula;
+            matrixAlgebraRotation;
+            matrixAlgebraCholesky;
+            matrixAlgebraLyapunovComparison;
\ No newline at end of file
diff --git a/README.md b/README.md
index fda08c9..8840c92 100644
--- a/README.md
+++ b/README.md
@@ -129,7 +129,6 @@ Please feel free to use this for teaching or learning purposes; however, taking
 </details>
 
 
-<!---
 <details>
   <summary> Week 6: Multivariate Time Series Concepts</summary>
 
@@ -140,17 +139,20 @@ Familiarize yourself with
 * important matrix concepts such as Eigenvalues, Kronecker product, orthogonality, rotation matrices, Cholesky decomposition and Lyapunov equations
 * multivariate notation and dimensions of vectors and matrices for VAR(p) models
 * autocovariances, stability and covariance-stationarity in multivariate VAR(p) models
-* the companion form
+* the companion form of a VAR(p) model
 
 ### To Do
 
-* [x] Review the solutions of [last week's exercises](https://github.com/wmutschl/Quantitative-Macroeconomics/releases/latest/download/week_5.pdf) (except the bootstrap one) and write down all your questions
+* [x] Review the solutions of [last week's exercises](https://github.com/wmutschl/Quantitative-Macroeconomics/releases/latest/download/week_5.pdf) and write down all your questions
 * [x] Read Kilian and Lütkepohl (2007, Ch. 2.2) and Lütkepohl (2005, Chapter 2 and Appendix A); make note of all the aspects and concepts that you are not familiar with or that you find difficult to understand
-* [x] Do exercise sheet 6 (the solutions are already available)
+* [x] Do exercise 1 of week 6
 * [x] If you have questions, get in touch with me via email or (better) [schedule a meeting](https://schedule.mutschler.eu)
 
 </details>
 
+
+<!---
+
 <details>
   <summary> Week 7: Estimating VAR model with OLS and ML; The identification problem in SVAR models</summary>
 
diff --git a/exercises/dimensions_and_var_one_representation.tex b/exercises/dimensions_and_var_one_representation.tex
index 3978611..d1cbd9d 100644
--- a/exercises/dimensions_and_var_one_representation.tex
+++ b/exercises/dimensions_and_var_one_representation.tex
@@ -1,6 +1,6 @@
-\section[Dimensions and VAR(1) representation]{Dimensions and VAR(1) representation\label{ex:DimensionsAndVAROneRepresentation}}
+\section[Dimensions and VAR{(1)} representation]{Dimensions and VAR{(1)} representation\label{ex:DimensionsAndVAROneRepresentation}}
 Let \(y_t\) be a K-dimensional covariance stationary random vector.
-Consider the VAR(p)-process
+Consider the VAR{(p)}-process
 \begin{align*}
 y_t = \nu + \sum_{i=1}^p A_i {y_{t-i}} + u_t
 \end{align*}
@@ -10,22 +10,23 @@
 \item Assume that \(E(u_t) = 0; E(u_t u_t') = \Sigma_u\) with \(\Sigma_u\) being symmetric and positive definite.
 Which additional assumptions do we need to assure that \(u_t\) is a multivariate white noise process?	
 
-\item Consider a VAR(2) model with \(K=4\) variables and a constant term.
+\item Consider a VAR{(2)} model with \(K=4\) variables and a constant term.
 How many parameters do we need to estimate?
 
-\item Show how to represent a VAR(3) model as a VAR(1) model. Hint: stack \(y_t, y_{t-1}\) and \(y_{t-2}\) into a vector.
+\item Show how to represent a VAR{(3)} model as a VAR{(1)} model.
+Hint: stack \(y_t, y_{t-1}\) and \(y_{t-2}\) into a vector.
 
-\item Write a function to compute the \enquote{companion VAR(1) form} of any VAR(p) model with constant term.
+\item Write a function to compute the \enquote{companion VAR{(1)} form} of any VAR{(p)} model with constant term.
 \end{enumerate}
 
 \paragraph{Readings}
 \begin{itemize}
-	\item \textcite[Ch.~2.2]{Kilian.Lutkepohl_2017_StructuralVectorAutoregressive}
-	\item \textcite[Ch.~2]{Lutkepohl_2005_NewIntroductionMultiple}
+\item \textcite[Ch.~2.2]{Kilian.Lutkepohl_2017_StructuralVectorAutoregressive}
+\item \textcite[Ch.~2]{Lutkepohl_2005_NewIntroductionMultiple}
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:DimensionsAndVAROneRepresentation}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/dimensions_and_var_one_representation_solution.tex}
 \fi
 \newpage
diff --git a/exercises/dimensions_and_var_one_representation_solution.tex b/exercises/dimensions_and_var_one_representation_solution.tex
index baf9e47..890d054 100644
--- a/exercises/dimensions_and_var_one_representation_solution.tex
+++ b/exercises/dimensions_and_var_one_representation_solution.tex
@@ -1,34 +1,35 @@
 \begin{enumerate}
-\item \(\nu\) snd \(u_t\) are both K-dimensional vectors: \(\nu,u_t \in \mathbb{R}^{K \times 1}\).
+\item \(\nu \) and \(u_t\) are both K-dimensional vectors: \(\nu,u_t \in \mathbb{R}^{K \times 1}\).
 \(A_i\) is a \(K \times K\) matrix.
 
 \item We must have \({\Gamma_u(h)} = Cov(u_t, u_{t-h}) = 0_{K\times K}\) for any \(h\neq0\),
   that is all autocovariances are zero
   (except for \(h=0\) which is the covariance matrix).
 Importantly: we do not need a distributional assumption!
-	
+
 \item General: \(K\) constants + \(K^2\cdot p\) autoregressive coefficients + \(K(K+1)/2\) covariance terms (due to symmetry).
-Here: \(4+4^2\cdot2+4\cdot(4+1)/2=46\).
+Here: \(4 + 4^2 \cdot 2 + 4 \cdot (4+1)/2 = 46\).
 That's a lot!
 Therefore we will try to restrict some parameters (e.g.\ set equal to zero or by using Bayesian priors)
-or consider only small VAR systems, e.g. \(K=3\) or \(p=1\), etc.
+  or consider only small VAR systems, e.g.\
+  \(K=3\) or \(p=1\), etc.
 
-\item VAR(3): \(y_t = \nu + A_1 y_{t-1} + A_2 y_{t-2} + A_3 y_{t-3} + u_t\).
+\item VAR{(3)}: \(y_t = \nu + A_1 y_{t-1} + A_2 y_{t-2} + A_3 y_{t-3} + u_t\).
 Idea: Stack \(y_t, y_{t-1}\) and \(y_{t-2}\) into a vector and note that \(y_{t-1}=y_{t-1}\) and \(y_{t-2}=y_{t-2}\).
 That is
 \begin{align*}
-\underbrace{\begin{bmatrix} y_t\\ y_{t-1} \\ y_{t-2} \end{bmatrix}}_{\widetilde{y}_t}
+\underbrace{\begin{bmatrix} y_t \\ y_{t-1} \\ y_{t-2} \end{bmatrix}}_{\widetilde{y}_t}
 = \underbrace{\begin{bmatrix} \nu \\ 0 \\ 0 \end{bmatrix}}_{\widetilde{\nu}_t}
-+ \underbrace{\begin{bmatrix} A_1 & A_2 & A_3 \\ I & 0 & 0\\ 0&I&0\end{bmatrix}}_{\widetilde{A}}
-  \underbrace{\begin{bmatrix} y_{t-1}\\ y_{t-2} \\ y_{t-3} \end{bmatrix}}_{\widetilde{y}_{t-1}}
-+ \underbrace{\begin{bmatrix} u_t \\ 0 \\ 0\end{bmatrix}}_{\widetilde{u}_t}
++ \underbrace{\begin{bmatrix} A_1 & A_2 & A_3 \\ I & 0 & 0 \\ 0 & I & 0 \end{bmatrix}}_{\widetilde{A}}
+  \underbrace{\begin{bmatrix} y_{t-1} \\ y_{t-2} \\ y_{t-3} \end{bmatrix}}_{\widetilde{y}_{t-1}}
++ \underbrace{\begin{bmatrix} u_t \\ 0 \\ 0 \end{bmatrix}}_{\widetilde{u}_t}
 \end{align*}
 where \(I\) is the \(K\)-dimensional identity matrix and \(0\) the \(K\)-dimensional zero matrix.
 Therefore: \(\widetilde{y}_t = \widetilde{A} \widetilde{y}_{t-1} + \widetilde{u}_t\).
-This is called the Companion Form.
-It is particularly useful, when checking the stability and covariance-stationarity properties of VAR(p) processes 
-as we can simply compute the Eigenvalues of \(\widetilde{A}\)
-and check whether all of them are inside the unit circle, i.e.\ between \(-1\) and \(1\).
+This is called the \emph{Companion Form}.
+It is particularly useful, when checking the stability and covariance-stationarity properties of VAR{(p)} processes 
+  as we can simply compute the Eigenvalues of \(\widetilde{A}\)
+  and check whether all of them are inside the unit circle, i.e.\ between \(-1\) and \(1\).
 No need to find the roots of the general Lag-polynomials.
 
 \item \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/companionForm.m}
diff --git a/exercises/matrix_algebra.tex b/exercises/matrix_algebra.tex
index 4791d3f..fe70c08 100644
--- a/exercises/matrix_algebra.tex
+++ b/exercises/matrix_algebra.tex
@@ -15,7 +15,7 @@
 \item Consider the matrices D:\@ \(m\times n\), E:\@ \(n\times p\) and F:\@ \(p\times k\).
 Show that
 \[vec(DEF)=\left(F'\otimes D\right) vec(E),\]
-where \(\otimes\) is the Kronecker product and \(vec\) the vectorization operator
+where \(\otimes \) is the Kronecker product and \(vec\) the vectorization operator
 either on paper or using a symbolic toolbox.
 
 \item Show that R is an orthogonal matrix. Why is this matrix called a rotation matrix?	
@@ -30,28 +30,28 @@
 	\begin{enumerate}
 	\item the Kronecker product and vectorization
 	\item the following iterative algorithm:
-		\begin{align*}
-		\Sigma_{y,0} &= I, A_0 = A, \Sigma_{u,0} = \Sigma_{u}\\
-		\Sigma_{y,i+1} &= A_i \Sigma_{y,i} A_i' + \Sigma_{u,i}\\
-		\Sigma_{u,i+1} &= A_i \Sigma_{u,i} A_i' + \Sigma_{u,i}\\
-		A_{i+1} &= A_i A_i
-		\end{align*}
-		Write a loop until either a maximal number of iterations (say 500) is reached
-		or each element of \(\Sigma_{y,i+1}-\Sigma_{y,i}\) is less than \(10^{-25}\) in absolute terms.
+	\begin{align*}
+	\Sigma_{y,0} &= I, A_0 = A, \Sigma_{u,0} = \Sigma_{u}\\
+	\Sigma_{y,i+1} &= A_i \Sigma_{y,i} A_i' + \Sigma_{u,i}\\
+	\Sigma_{u,i+1} &= A_i \Sigma_{u,i} A_i' + \Sigma_{u,i}\\
+	A_{i+1} &= A_i A_i
+	\end{align*}
+	Write a loop until either a maximal number of iterations (say 500) is reached
+	  or each element of \(\Sigma_{y,i+1}-\Sigma_{y,i}\) is less than \(10^{-25}\) in absolute terms.
 	\item Compare both approaches for A and \(\Sigma_u\) given above.
 	\end{enumerate}
 \end{enumerate}
 
 \paragraph{Readings:}
 \begin{itemize}	
-	\item \textcite[Ch.~4.2]{Anderson.McGrattan.Hansen.EtAl_1996_MechanicsFormingEstimating}
-	\item \textcite[Ch.~6.7]{Anderson.Moore_1979_OptimalFiltering}
-	\item \textcite[App.~A]{Lutkepohl_2005_NewIntroductionMultiple}
-	\item \textcite[Ch.~4.10]{Uribe.Schmitt-Grohe_2017_OpenEconomyMacroeconomics}
+\item \textcite[Ch.~4.2]{Anderson.McGrattan.Hansen.EtAl_1996_MechanicsFormingEstimating}
+\item \textcite[Ch.~6.7]{Anderson.Moore_1979_OptimalFiltering}
+\item \textcite[App.~A]{Lutkepohl_2005_NewIntroductionMultiple}
+\item \textcite[Ch.~4.10]{Uribe.Schmitt-Grohe_2017_OpenEconomyMacroeconomics}
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:MatrixAlgebra}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/matrix_algebra_solution.tex}
 \fi
 \newpage
diff --git a/exercises/matrix_algebra_solution.tex b/exercises/matrix_algebra_solution.tex
index 483f26c..27ac820 100644
--- a/exercises/matrix_algebra_solution.tex
+++ b/exercises/matrix_algebra_solution.tex
@@ -1,9 +1,10 @@
 \begin{enumerate}
 \item \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/matrixAlgebraEigenvalues.m}
-In the univariate AR(1) model we would check whether the autocorrelation coefficient is between -1 and 1,
-  i.e.\ whether \(|\phi| = |A|<1\) such that \(\sum_{j=0}^\infty (AL)^j=1/(1-AL)\) where \(L\) is the lag operator.
+In the univariate AR{(1)} model we would check whether the autocorrelation coefficient is between -1 and 1,
+  i.e.\ whether \(|\phi| = |A|<1\) such that \(\sum_{j=0}^\infty {(AL)}^j=1/(1-AL)\)
+  where \(L\) is the lag operator.
 In the multivariate case, we want to check the same thing,
-  i.e. \(\sum_{j=0}^\infty (AL)^j=(1-AL)^{-1}\).
+  i.e.| \(\sum_{j=0}^\infty {(AL)}^j={(1-AL)}^{-1}\).
 Note that \(A\) is a square matrix and taking the power of a matrix is not a trivial task.
 One convenient way to do so, is to consider an eigenvalue decomposition (if it exists):
 \[A= Q \Lambda Q^{-1}\]
@@ -12,87 +13,191 @@
 Moreover, \(\Lambda \) is a diagonal matrix and \(Q\) is an orthogonal matrix \(Q^{-1}=Q'\).
 Using this decomposition one can show that it is very easy to compute any power of a matrix:
 \begin{itemize}
-    \item matrix inverse \(A^{-1} = Q \Lambda^{-1} Q^{-1}\) where the inverse of \([\Lambda^{-1}]_{ii} = 1/\lambda_i\) is very easy to calculate as it is a diagonal matrix
-    \item matrix powers: \(A^2=(Q\Lambda Q^{-1})(Q\Lambda Q^{-1})=Q\Lambda (Q^{-1}Q) \Lambda Q^{-1} = Q \Lambda^2 Q^{-1}\) or more generally: \(A^j = Q \Lambda^j Q^{-1}\).
+\item matrix inverse \(A^{-1} = Q \Lambda^{-1} Q^{-1}\) where the inverse of \({[\Lambda^{-1}]}_{ii} = 1/\lambda_i\) is very easy to calculate as it is a diagonal matrix
+\item matrix powers: \(A^2=(Q\Lambda Q^{-1})(Q\Lambda Q^{-1})=Q\Lambda (Q^{-1}Q) \Lambda Q^{-1} = Q \Lambda^2 Q^{-1}\) or more generally: \(A^j = Q \Lambda^j Q^{-1}\).
 \end{itemize}
-So, for \(\sum_{j=0}^\infty {(AL)}^j=(1-AL)^{-1}\) we need that \(\lim_{j\rightarrow \infty}\Lambda^j=0\).
+So, for \(\sum_{j=0}^\infty {(AL)}^j={(1-AL)}^{-1}\) we need that \(\lim_{j\rightarrow \infty}\Lambda^j=0\).
 As this is a diagonal matrix, the task simplifies as we only need to look at each eigenvalue whether it is between -1 and 1: \(|\lambda_i|<1\).
-In other words, for VAR(1) systems \(y_t = c + A y_{t-1} + u_t\) we need to check whether the eigenvalues of \(A\) are inside the unit circle.
-If they are, then the VAR(1) model is said to be both stable and covariance-stationary.
-	
+In other words, for VAR{(1)} systems \(y_t = c + A y_{t-1} + u_t\) we need to check whether the eigenvalues of \(A\) are inside the unit circle.
+If they are, then the VAR{(1)} model is said to be both stable and covariance-stationary.
+
 \item Example for vectorization and Kronecker product:
 \begin{align*}
-    \underbrace{vec\begin{pmatrix} 1&3&2\\1&0&0\\1&2&2 \end{pmatrix}}_{3\times3} = \underbrace{\begin{pmatrix} 1 \\1 \\1 \\3 \\0 \\2 \\2 \\ 0 \\2\end{pmatrix}}_{9\times1}, \qquad 
-    \underbrace{\begin{pmatrix} 1&3&2\\1&0&0\\1&2&2 \end{pmatrix}}_{3\times3} \otimes \underbrace{\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}}_{3\times2} =
-    \underbrace{\begin{pmatrix} 1\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}&3\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}&2\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}\\1\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}&0\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}&0\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}\\1\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}&2\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}&2\cdot\begin{pmatrix}0&5\\5&0\\1&1 \end{pmatrix}  \end{pmatrix}}_{9\times6}
+\underbrace{vec
+  \begin{pmatrix}
+  1&3&2\\
+  1&0&0\\
+  1&2&2
+  \end{pmatrix}
+}_{3\times3}
+=
+\underbrace{%
+  \begin{pmatrix}1 \\1 \\1 \\3 \\0 \\2 \\2 \\ 0 \\2\end{pmatrix}
+}_{9\times1}
+,\qquad 
+\underbrace{%
+  \begin{pmatrix}
+  1&3&2\\
+  1&0&0\\
+  1&2&2
+  \end{pmatrix}
+}_{3\times3}
+\otimes
+\underbrace{%
+  \begin{pmatrix}
+  0&5\\
+  5&0\\
+  1&1
+  \end{pmatrix}
+}_{3\times2}
+=
+\underbrace{%
+  \begin{pmatrix}
+  1 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix} &
+  3 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix} &
+  2 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix}
+  \\
+  1 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix} &
+  0 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix} &
+  0 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix}
+  \\
+  1 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix}&
+  2 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix}&
+  2 \cdot \begin{pmatrix} 0 & 5 \\ 5 & 0 \\ 1 & 1 \end{pmatrix}
+  \end{pmatrix}
+}_{9\times6}
 \end{align*}
 Using this definition, we can show that \(vec(DEF) = (F' \otimes D) vec(E)\) using e.g.\ a symbolic toolbox:
 \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/matrixAlgebraKroneckerFormula.m}
-Of course you can do this on paper as well:		 
+Of course you can do this on paper as well:
+
+\begingroup\scriptsize
 \begin{align*}
 DEF &= D \begin{pmatrix} e_1 & e_2 & \cdots & e_p \end{pmatrix}
 \begin{pmatrix}
 f_{11} &f_{12} &\cdots &f_{1k} \\
 f_{21} &f_{22} &\cdots &f_{2k} \\
-\vdots &\vdots &\vdots &\vdots\\
+\vdots &\vdots &\vdots &\vdots \\
 f_{p1} &f_{p2} &\cdots &f_{pk}
-\end{pmatrix}\\
-&= D \underbrace{\begin{pmatrix} e_1f_{11}+e_2f_{21}+\cdots+e_p f_{p1},& e_1f_{12}+e_2f_{22}+\cdots+e_p f_{p2}, & \dots ,& e_1f_{1k}+e_2f_{2k}+\cdots+e_p f_{pk}\end{pmatrix}}_{n\times k}
+\end{pmatrix}
+\\
+&= D \underbrace{%
+  \begin{pmatrix}
+  e_1 f_{11} + e_2 f_{21} + \cdots + e_p f_{p1}, &
+  e_1 f_{12} + e_2 f_{22} + \cdots + e_p f_{p2}, &
+  \dots ,&
+  e_1 f_{1k} + e_2 f_{2k} + \cdots + e_p f_{pk}
+  \end{pmatrix}
+}_{n\times k}
 \end{align*}
+\endgroup
 Vectorizing:
 \begin{align*}
-vec(DEF) &= \begin{pmatrix} f_{11}D e_1 +f_{21}D e_2+\cdots+ f_{p1}D e_p\\ f_{12}D e_1+f_{22} D e_2 + \cdots +  f_{p2} D e_p \\ \vdots \\ f_{1k} D e_1+ f_{2k} D e_2 +\cdots+ f_{pk} D e_p  \end{pmatrix}
-= \begin{pmatrix} f_{11}D &  f_{21}D  & \cdots & f_{p1}D \\ f_{12}D  & f_{22} D & \cdots & f_{p2} D\\ \vdots & \vdots &\vdots&\vdots \\ f_{1k}D & f_{2k} D &\cdots& f_{pk} D  \end{pmatrix} \begin{pmatrix} e_1\\e_2\\ \vdots \\ e_p\end{pmatrix}\\
+vec(DEF) &=
+\begin{pmatrix}
+f_{11} D e_1 + f_{21} D e_2 + \cdots + f_{p1} D e_p \\
+f_{12} D e_1 + f_{22} D e_2 + \cdots + f_{p2} D e_p \\
+\vdots \\
+f_{1k} D e_1 + f_{2k} D e_2 + \cdots + f_{pk} D e_p
+\end{pmatrix}
+=
+\begin{pmatrix}
+f_{11} D & f_{21} D & \cdots & f_{p1} D \\
+f_{12} D & f_{22} D & \cdots & f_{p2} D \\
+\vdots & \vdots & \vdots & \vdots \\
+f_{1k}D & f_{2k} D & \cdots & f_{pk} D
+\end{pmatrix}
+\begin{pmatrix} e_1 \\ e_2 \\ \vdots \\ e_p \end{pmatrix}
+\\
 &= \left(F'\otimes D\right) vec(E)
 \end{align*}
 
 \item An orthogonal matrix is characterized by \(R'=R^{-1}\) and therefore \(R'R=R R' = I\).
 Here:
 \begin{align*}
-R'R = \begin{pmatrix}
-(\cos(\phi))^2 + (\sin(\phi))^2 & -\cos(\phi)\sin(\phi) + \sin(\phi)\cos(\phi)\\-\sin(\phi)\cos(\phi) + \cos(\phi)\sin(\phi) & (\sin(\phi))^2 + (\cos(\phi))^2
+R'R =
+\begin{pmatrix}
+{(\cos(\phi))}^2 + {(\sin(\phi))}^2 & -\cos(\phi)\sin(\phi) + \sin(\phi)\cos(\phi)
+\\
+-\sin(\phi)\cos(\phi) + \cos(\phi)\sin(\phi) & {(\sin(\phi))}^2 + {(\cos(\phi))}^2
 \end{pmatrix}
 \end{align*}
-with \((\cos(\phi))^2 + (\sin(\phi))^2 = 1\) (so-called trigonometric Pythagoras).
-		 
+with \({(\cos(\phi))}^2 + {(\sin(\phi))}^2 = 1\) (so-called trigonometric Pythagoras).
+
 \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/matrixAlgebraRotation.m}
-		 
+
 \(R\) is called a rotation matrix,
   because it rotates vectors or objects in the Euclidian space without stretching or shrinking the object.
-\begin{center}  \includegraphics[width=.5\textwidth]{plots/Rotation.png} \end{center}
-In this example the matrix R rotates the vector counter-clockwise given angle \(\phi\).
-An active rotation means that the vector is multiplied by the rotation matrix and this rotates the vector counterclockwise \(x' = Rx\).
+\begin{center}
+\includegraphics[width=.5\textwidth]{plots/Rotation.png}
+\end{center}
+In this example the matrix R rotates the vector counter-clockwise given angle \(\phi \).
+An active rotation means that the vector is multiplied by the rotation matrix
+  and this rotates the vector counterclockwise \(x' = Rx\).
 A passive rotation means that the coordinate system is rotated and therefore the vector is also rotated: \(x' = R^{-1} x\).
 Later on we will need rotation matrices for identification of structural shocks!
 
 \item \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/matrixAlgebraCholesky.m}
 \begin{align*}
-\underbrace{\begin{pmatrix}1&0&0\\0&1&0\\0&0.5&1\end{pmatrix}}_W \underbrace{\begin{pmatrix}2.25&0&0\\0&1&0\\0&0&0.49\end{pmatrix}}_{\Sigma_\varepsilon} \underbrace{\begin{pmatrix}1&0&0\\0&1&0.5\\0&0&1\end{pmatrix}}_{W'} = \underbrace{\begin{pmatrix}2.25&0&0\\0&1&0.5\\0&0.5&0.74\end{pmatrix}}_{\Sigma}
+\underbrace{%
+  \begin{pmatrix}
+  1 & 0   & 0 \\
+  0 & 1   & 0 \\
+  0 & 0.5 & 1
+  \end{pmatrix}
+}_W
+\underbrace{%
+  \begin{pmatrix}
+  2.25 & 0 & 0 \\
+  0    & 1 & 0 \\
+  0    & 0 & 0.49
+  \end{pmatrix}
+}_{\Sigma_\varepsilon}
+\underbrace{%
+  \begin{pmatrix}
+  1 & 0 & 0   \\
+  0 & 1 & 0.5 \\
+  0 & 0 & 1
+  \end{pmatrix}
+}_{W'}
+=
+\underbrace{%
+  \begin{pmatrix}
+  2.25 & 0  &  0   \\
+  0    & 1   & 0.5 \\
+  0    & 0.5 & 0.74
+  \end{pmatrix}
+}_{\Sigma}
 \end{align*}
 
 \item Solving this equation can be done either analytically or using an algorithm:
+
 \begin{enumerate}
-    \item Analytically:
-        \begin{align*}
-            vec(\Sigma_y) &= vec(A \Sigma_y A') + vec(\Sigma_u) = (A \otimes A)vec(\Sigma_y) + vec(\Sigma_u)\\
-            (I-A\otimes A)vec(\Sigma_y) &= vec(\Sigma_u)\\
-            vec(\Sigma_y) &= (I-A\otimes A)^{-1}vec(\Sigma_u)
-        \end{align*}
-    \item Doubling algorithm:
-    \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/dlyapdoubling.m}
-    The basic idea of the doubling algorithm is to start at some \(\Sigma_{y,0}\)
-    and find new values for \(\Sigma_{y,i+1}\) using the equation \(A \Sigma_{y,i} A' + \Sigma_u\)
-    until the difference \(\Sigma_{y,i+1} - \Sigma_{y,i}\) becomes very small
-    or a certain maximum number of iterations is reached.
-    
-    The doubling algorithm, however, allows one to pass in one iteration
-    from \(\Sigma_{y,i}\) to \(\Sigma_{y,2i}\) rather than \(\Sigma_{y,i+1}\),
-    provided that one updates three other matrices.
-    There are also other (generalized) algorithms to solve such matrix Lyapunov (or Sylvester) equations.
 
-    \item Comparison:
-    \lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/matrixAlgebraLyapunovComparison.m}
-    The doubling algorithm is faster than the analytical closed-form expression based on the Kronecker product.
+\item Analytically:
+\begin{align*}
+vec(\Sigma_y) &= vec(A \Sigma_y A') + vec(\Sigma_u) = (A \otimes A)vec(\Sigma_y) + vec(\Sigma_u)
+\\
+(I-A\otimes A)vec(\Sigma_y) &= vec(\Sigma_u)
+\\
+vec(\Sigma_y) &= {(I-A\otimes A)}^{-1}vec(\Sigma_u)
+\end{align*}
+
+\item Doubling algorithm:
+\lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/dlyapdoubling.m}
+The basic idea of the doubling algorithm is to start at some \(\Sigma_{y,0}\)
+  and find new values for \(\Sigma_{y,i+1}\) using the equation \(A \Sigma_{y,i} A' + \Sigma_u\)
+  until the difference \(\Sigma_{y,i+1} - \Sigma_{y,i}\) becomes very small
+  or a certain maximum number of iterations is reached.
+
+The doubling algorithm, however, allows one to pass in one iteration
+  from \(\Sigma_{y,i}\) to \(\Sigma_{y,2i}\) rather than \(\Sigma_{y,i+1}\),
+  provided that one updates three other matrices.
+There are also other (generalized) algorithms to solve such matrix Lyapunov (or Sylvester) equations.
+
+\item Comparison:
+\lstinputlisting[style=Matlab-editor,basicstyle=\mlttfamily,title=\lstname]{progs/matlab/matrixAlgebraLyapunovComparison.m}
+The doubling algorithm is faster than the analytical closed-form expression based on the Kronecker product.
 \end{enumerate}
-		
+
 \end{enumerate}
\ No newline at end of file
diff --git a/exercises/understanding_multivariate_concepts.tex b/exercises/understanding_multivariate_concepts.tex
index bd2525e..d1a9962 100644
--- a/exercises/understanding_multivariate_concepts.tex
+++ b/exercises/understanding_multivariate_concepts.tex
@@ -1,10 +1,19 @@
 \section[Understanding multivariate time series concepts]{Understanding multivariate time series concepts\label{ex:UnderstandingMultivariateTimeSeriesConcepts}}
 Let \(y_t\) be a K-dimensional time series and \(u_t\) a K-dimensional white noise process.
+
 \begin{enumerate}
+
 \item Why are we concerned with multivariate time series?
-For example, why do we model the VAR(1) process
+For example, why do we model the VAR{(1)} process
 \begin{align*}
-\begin{pmatrix}y_{1,t}\\ y_{2,t}\end{pmatrix} = \begin{pmatrix} c_1 \\ c_2\end{pmatrix} + \begin{pmatrix}a_{11} & a_{12}\\ a_{21} & a_{22} \end{pmatrix} \begin{pmatrix}y_{1,{t-1}}\\ y_{2,{t-1}}\end{pmatrix} + \begin{pmatrix}u_{1,t}\\ u_{2,t}\end{pmatrix}
+\begin{pmatrix} y_{1,t} \\ y_{2,t} \end{pmatrix}
+=
+\begin{pmatrix} c_1 \\ c_2 \end{pmatrix}
++
+\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}
+\begin{pmatrix} y_{1,{t-1}} \\ y_{2,{t-1}} \end{pmatrix}
++
+\begin{pmatrix} u_{1,t} \\ u_{2,t}\end{pmatrix}
 \end{align*}
 simultaneously instead of two models for each variable separately?
 
@@ -12,16 +21,21 @@
 
 \item How does the definition of covariance stationary change in the multivariate case?
 
-\item Consider the following VAR(1) process \(y_t = c + A y_{t-1} + u_t\)
+\item Consider the following VAR{(1)} process \(y_t = c + A y_{t-1} + u_t\)
 \begin{align*}
-\begin{pmatrix}y_{1,t} \\ y_{2,t}\\y_{3,t} \end{pmatrix} &= \begin{pmatrix}0\\0\\0 \end{pmatrix} + \begin{pmatrix}0.5 &0 &0 \\0.1&0.1&0.3\\0&0.2&0.3 \end{pmatrix} \begin{pmatrix}y_{1,{t-1}} \\ y_{2,{t-1}}\\y_{3,{t-1}} \end{pmatrix} + \begin{pmatrix}u_{1,t} \\ u_{2,t}\\ u_{3,t} \end{pmatrix}
+\begin{pmatrix} y_{1,t} \\ y_{2,t} \\ y_{3,t} \end{pmatrix}
+&= \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}
++ \begin{pmatrix} 0.5 & 0 & 0 \\ 0.1 & 0.1 & 0.3 \\ 0 & 0.2 & 0.3 \end{pmatrix}
+\begin{pmatrix} y_{1,{t-1}} \\ y_{2,{t-1}} \\ y_{3,{t-1}} \end{pmatrix}
++ \begin{pmatrix} u_{1,t} \\ u_{2,t} \\ u_{3,t} \end{pmatrix}
 \end{align*}
 provided that \(u_t \sim WN(0,\Sigma_u)\) and
 \begin{align*}
-	\Sigma_u = \begin{pmatrix}2.25 & 0 & 0\\ 0 & 1 & 0.5\\ 0 & 0.5 & 0.74 \end{pmatrix}
+\Sigma_u = \begin{pmatrix} 2.25 & 0 & 0 \\ 0 & 1 & 0.5 \\ 0 & 0.5 & 0.74 \end{pmatrix}
 \end{align*}
-Compute the coefficients \(\Phi_0, \Phi_1, \dots \in \mathbb{R}^{3\times 3}\) of the lag polynomial \(\Phi(L) := \sum_{i=0}^\infty \Phi_i L^i\),
-and a \(\nu \in \mathbb{R}^3\) such that we get the following \(MA(\infty)\) process:
+Compute the coefficients \(\Phi_0, \Phi_1, \dots \in \mathbb{R}^{3\times 3}\)
+  of the lag polynomial \(\Phi(L) := \sum_{i=0}^\infty \Phi_i L^i\),
+  and a \(\nu \in \mathbb{R}^3\) such that we get the following \(MA(\infty)\) process:
 \begin{align*}
 y_t = \nu + \Phi(L) u_t
 \end{align*}
@@ -30,11 +44,11 @@
 
 \paragraph{Readings}
 \begin{itemize}
-	\item \textcite[Ch.~2]{Lutkepohl_2005_NewIntroductionMultiple}
+\item \textcite[Ch.~2]{Lutkepohl_2005_NewIntroductionMultiple}
 \end{itemize}
 
 \begin{solution}\textbf{Solution to \nameref{ex:UnderstandingMultivariateTimeSeriesConcepts}}
-\ifDisplaySolutions
+\ifDisplaySolutions%
 \input{exercises/understanding_multivariate_concepts_solution.tex}
 \fi
 \newpage
diff --git a/exercises/understanding_multivariate_concepts_solution.tex b/exercises/understanding_multivariate_concepts_solution.tex
index 99dc74b..9daf9f8 100644
--- a/exercises/understanding_multivariate_concepts_solution.tex
+++ b/exercises/understanding_multivariate_concepts_solution.tex
@@ -17,37 +17,48 @@
 Therefore, \(E[y_t]\) is the unconditional expectation of \(y_t\) at period \(t\).
 The expected value as a linear operator can be dragged into a vector or matrix:
 \begin{align*}
-E[y_t] = E\left[\begin{pmatrix}y_{1,t} \\ \vdots \\ y_{K,t} \end{pmatrix} \right]
-= \begin{pmatrix}E[y_{1,t}] \\ \vdots \\ E[y_{K,t}] \end{pmatrix}
+E[y_t] = E\left[ \begin{pmatrix} y_{1,t} \\ \vdots \\ y_{K,t} \end{pmatrix} \right]
+= \begin{pmatrix} E[y_{1,t}] \\ \vdots \\ E[y_{K,t}] \end{pmatrix}
 \end{align*}
 
 \emph{Interpretation of \(\Gamma_y(h)\):}
 In the univariate case we defined the autocovariance as the covariance of a random variable with its own lagged values.
 In the multivariate case we also consider covariances between different variables and different points in time.
 The autocovariance matrix \({\Gamma_y(h)} := Cov[{y_{t},{y_{t-h}}}]\) summarizes this information up in a neat fashion
-and is therefore a powerful tool in multivariate time series analysis:
+  and is therefore a powerful tool in multivariate time series analysis:
 \begin{align*}
-&Cov[{y_{t},{y_{t-h}}}] = E\left[({y_{t}}-E[{{y_{t}}}]) ({y_{t-h}}-E[{{y_{t-h}}}])' \right]\\
-&= E\left[\begin{pmatrix}y_{1,t} - E[y_{1,t}] \\ \vdots \\ y_{K,t} - E[y_{K,t}] \end{pmatrix} \begin{pmatrix} y_{1,{t-h}} - E[y_{1,{t-h}}] & \cdots & y_{K,{t-h}} - E[y_{K,{t-h}}]  \end{pmatrix} \right]\\
+& Cov[{y_{t},{y_{t-h}}}] = E\left[({y_{t}}-E[{{y_{t}}}]) ({y_{t-h}}-E[{{y_{t-h}}}])' \right]
+\\
+&= E\left[\begin{pmatrix} y_{1,t} - E[y_{1,t}] \\ \vdots \\ y_{K,t} - E[y_{K,t}] \end{pmatrix}
+\begin{pmatrix} y_{1,{t-h}} - E[y_{1,{t-h}}] & \cdots & y_{K,{t-h}} - E[y_{K,{t-h}}]  \end{pmatrix} \right]
+\\
 &= E\left[\begin{pmatrix}
-(y_{1,t}- E[y_{1,t}])(y_{1,{t-h}} - E[y_{1,{t-h}}]) & \cdots & (y_{1,t} - E[y_{1,t}])(y_{K,{t-h}} - E[y_{K,{t-h}}])\\
-\vdots & \ddots & \vdots \\
-(y_{K,t}- E[y_{K,t}])(y_{1,{t-h}} - E[y_{1,{t-h}}]) & \cdots & (y_{K,t} - E[y_{K,t}])(y_{K,{t-h}} - E[y_{K,{t-h}}])
-\end{pmatrix} \right]\\
+(y_{1,t}- E[y_{1,t}]) (y_{1,{t-h}} - E[y_{1,{t-h}}]) & \cdots & (y_{1,t} - E[y_{1,t}]) (y_{K,{t-h}} - E[y_{K,{t-h}}])
+\\
+\vdots & \ddots & \vdots
+\\
+(y_{K,t}- E[y_{K,t}]) (y_{1,{t-h}} - E[y_{1,{t-h}}]) & \cdots & (y_{K,t} - E[y_{K,t}]) (y_{K,{t-h}} - E[y_{K,{t-h}}])
+\end{pmatrix} \right]
+\\
 &= \begin{pmatrix}
-E[(y_{1,t}- E[y_{1,t}])(y_{1,{t-h}} - E[y_{1,{t-h}}])] & \cdots & E[(y_{1,t} - E[y_{1,t}])(y_{K,{t-h}} - E[y_{K,{t-h}}])]\\
-\vdots & \ddots & \vdots\\
-E[(y_{K,t}- E[y_{K,t}])(y_{1,{t-h}} - E[y_{1,{t-h}}])] & \cdots & E[(y_{K,t} - E[y_{K,t}])(y_{K,{t-h}} - E[y_{K,{t-h}}])]
-\end{pmatrix}\\
+E[(y_{1,t}- E[y_{1,t}]) (y_{1,{t-h}} - E[y_{1,{t-h}}])] & \cdots & E[(y_{1,t} - E[y_{1,t}]) (y_{K,{t-h}} - E[y_{K,{t-h}}])]
+\\
+\vdots & \ddots & \vdots
+\\
+E[(y_{K,t}- E[y_{K,t}]) (y_{1,{t-h}} - E[y_{1,{t-h}}])] & \cdots & E[(y_{K,t} - E[y_{K,t}]) (y_{K,{t-h}} - E[y_{K,{t-h}}])]
+\end{pmatrix}
+\\
 &=\begin{pmatrix}
-Cov[y_{1,t},y_{1,{t-h}}] & \cdots & Cov[y_{1,t},y_{K,{t-h}}]\\
-\vdots & \ddots & \vdots\\
+Cov[y_{1,t},y_{1,{t-h}}] & \cdots & Cov[y_{1,t},y_{K,{t-h}}]
+\\
+\vdots & \ddots & \vdots
+\\
 Cov[y_{K,t},y_{1,{t-h}}] & \cdots & Cov[y_{K,t},y_{K,{t-h}}]
 \end{pmatrix}
 \end{align*}
 On the diagonals we have the autocovariance of each variable,
   on the off-diagonals we have the covariances between the different variables.
-	
+
 \item Basically it is the same:
 A stochastic process is called weakly stationary (or covariance stationary),
   if for each period in time it has the same expectation independent of time
@@ -57,40 +68,49 @@
 \\
 \texttt{Definition}: The K-dimensional stochastic process \(y_t\) is called covariance stationary, if for all \(h,t,\tau \in \mathbb{Z}\):
 \begin{align}
-E[{y_t}] &= E[{y_\tau}]\\
+E[{y_t}] &= E[{y_\tau}]
+\\
 Cov(y_{t},y_{t-h}) &= Cov(y_{t+\tau}, y_{t-h+\tau}) \label{gammas}
 \end{align}
 
-\item We will use the \textbf{method of matching coefficients} to transform the VAR(1) model into a VMA(\(\infty\)) representation.
+\item We will use the \textbf{method of matching coefficients} to transform the VAR{(1)} model into a VMA{(\(\infty \))} representation.
 \begin{align*}
-	y_t &= A y_{t-1} + u_t\\
-	\underbrace{(I_3 - A L)}_{A(L)} y_t &= u_t\\
-	A(L) y_t &= u_t \\
-	{A(L)}^{-1}A(L) y_t &= {A(L)}^{-1} u_t\\
-	y_t &= {A(L)}^{-1} u_t = \nu + \Phi(L) u_t\\
-	\Rightarrow & \nu= 0, \Phi(L) = {A(L)}^{-1}
+y_t &= A y_{t-1} + u_t
+\\
+\underbrace{(I_3 - A L)}_{A(L)} y_t &= u_t
+\\
+A(L) y_t &= u_t
+\\
+{A(L)}^{-1}A(L) y_t &= {A(L)}^{-1} u_t
+\\
+y_t &= {A(L)}^{-1} u_t = \nu + \Phi(L) u_t
+\\
+\Rightarrow & \nu= 0, \Phi(L) = {A(L)}^{-1}
 \end{align*}
 In the method of matching coefficient we compare the coefficient matrices multiplied to each power of \(L\).
 That is, the expression on the left hand side has to match the expression on the right hand side.
 In our case:
 \begin{align*}
-	\Phi(L) &= {A(L)}^{-1}\\
-	A(L) \Phi(L) &= I_3\\
-	(I_3 - A L) \left(\sum_{i=0}^\infty \Phi_i L^i\right) &= I_3
+\Phi(L) &= {A(L)}^{-1}
+\\
+A(L) \Phi(L) &= I_3
+\\
+(I_3 - A L) \left(\sum_{i=0}^\infty \Phi_i L^i\right) &= I_3
 \end{align*}
 \begin{align*}
-	\Phi_0 L^0 &+ \Phi_1 L^1 + \Phi_2 L^2 + \dots \\
-	& - A \phi_0 L^1 - A \phi_1 L^2 - \cdots = I_3 L^0
+\Phi_0 L^0 &+ \Phi_1 L^1 + \Phi_2 L^2 + \dots
+\\
+& - A \phi_0 L^1 - A \phi_1 L^2 - \cdots = I_3 L^0
 \end{align*}
 \begin{align*}
-	L^0&: \Phi_0 &= I_3 \Rightarrow& \Phi_0 = I_3 = \begin{pmatrix}1&0&0\\0&1&0\\0&0&1 \end{pmatrix}\nonumber
-	\\
-	L^1&: \Phi_1 - A \Phi_0 &= 0 \Rightarrow& \Phi_1 = A \Phi_0 = A = \begin{pmatrix}0.5&0&0\\0.1&0.1&0.3\\0&0.2&0.3 \end{pmatrix}\nonumber
-	\\
-	L^2&: \Phi_2 - A \Phi_1 &= 0 \Rightarrow& \Phi_2 = A \Phi_1 = A^2 = \begin{pmatrix}0.25&0&0\\0.06&0.07&0.12\\0.02&0.08&0.15 \end{pmatrix}\nonumber
-	\\
-	\vdots\nonumber
-	\\
-	&\text{In general}: \Phi_s = A^s
+L^0&: \Phi_0 &= I_3 \Rightarrow& \Phi_0 = I_3 = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\nonumber
+\\
+L^1&: \Phi_1 - A \Phi_0 &= 0 \Rightarrow& \Phi_1 = A \Phi_0 = A = \begin{pmatrix} 0.5 & 0 & 0 \\ 0.1 & 0.1 & 0.3 \\ 0 & 0.2 & 0.3 \end{pmatrix}\nonumber
+\\
+L^2&: \Phi_2 - A \Phi_1 &= 0 \Rightarrow& \Phi_2 = A \Phi_1 = A^2 = \begin{pmatrix} 0.25 & 0 & 0 \\ 0.06 & 0.07 & 0.12 \\ 0.02 & 0.08 & 0.15 \end{pmatrix}\nonumber
+\\
+\vdots\nonumber
+\\
+&\text{In general}: \Phi_s = A^s
 \end{align*}
 \end{enumerate}
\ No newline at end of file
diff --git a/week_6.tex b/week_6.tex
new file mode 100644
index 0000000..f1ffd7c
--- /dev/null
+++ b/week_6.tex
@@ -0,0 +1,30 @@
+% !TEX root = week_6.tex
+\input{exercises/_common_header.tex}
+\Newassociation{solution}{Solution}{week_6_solution}
+\newif\ifDisplaySolutions\DisplaySolutionstrue%
+
+\begin{document}
+\title{Quantitative Macroeconomics\\~\\Winter 2024/25\\~\\Week 6}
+\author{Willi Mutschler\\willi@mutschler.eu}
+\date{Version: 1.0\\Latest version available on: \href{https://github.com/wmutschl/Quantitative-Macroeconomics/releases/latest/download/week_6.pdf}{GitHub}}
+\maketitle\thispagestyle{empty}
+
+\newpage
+\Opensolutionfile{week_6_solution}[week_6_solution]
+\tableofcontents\thispagestyle{empty}\newpage
+
+\setcounter{page}{1}
+\input{exercises/matrix_algebra.tex}\newpage
+\input{exercises/understanding_multivariate_concepts.tex}\newpage
+\input{exercises/dimensions_and_var_one_representation.tex}\newpage
+\printbibliography%
+\newpage
+
+\Closesolutionfile{week_6_solution}
+\ifDisplaySolutions%
+\newpage
+\appendix
+\section{Solutions}
+\input{week_6_solution}
+\fi
+\end{document}
\ No newline at end of file