diff --git a/README.md b/README.md
index 773970cb..cb19a814 100644
--- a/README.md
+++ b/README.md
@@ -3,7 +3,7 @@
 `pyerrors` is a python package for error computation and propagation of Markov chain Monte Carlo data.
 
 - **Documentation:** https://fjosw.github.io/pyerrors/pyerrors.html
-- **Examples**: https://github.com/fjosw/pyerrors/tree/develop/examples (Do not work properly at the moment)
+- **Examples**: https://github.com/fjosw/pyerrors/tree/develop/examples
 - **Contributing:** https://github.com/fjosw/pyerrors/blob/develop/CONTRIBUTING.md
 - **Bug reports:** https://github.com/fjosw/pyerrors/issues
 
diff --git a/examples/05_matrix_operations.ipynb b/examples/05_matrix_operations.ipynb
index f2a75aa1..926d1734 100644
--- a/examples/05_matrix_operations.ipynb
+++ b/examples/05_matrix_operations.ipynb
@@ -51,7 +51,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The standard matrix product can be performed with @"
+    "The standard matrix product can be performed with `@`"
    ]
   },
   {
@@ -106,7 +106,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -131,7 +131,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -151,12 +151,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "For a vector of `Obs`, we again use np.asarray to end up with the correct object"
+    "For a vector of `Obs`, we again use `np.asarray` to end up with the correct object"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -212,7 +212,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -233,13 +233,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Matrix to matrix operations\n",
-    "For matrix operations with a matrix as return value we can use another wrapper `mat_mat_op`. Take as an example the cholesky decompostion. __Here we need to use the autograd wrapped version of numpy__ (imported as anp) to use automatic differentiation."
+    "The cholesky decomposition can be obtained as follows"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -267,7 +266,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -293,7 +292,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -301,7 +300,7 @@
      "output_type": "stream",
      "text": [
       "[[Obs[0.494(12)] Obs[0.0]]\n",
-      " [Obs[0.280(39)] Obs[1.150(38)]]]\n",
+      " [Obs[0.280(40)] Obs[1.150(39)]]]\n",
       "Check:\n",
       "[[Obs[1.0] Obs[0.0]]\n",
       " [Obs[0.0] Obs[1.0]]]\n"
@@ -328,7 +327,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -336,10 +335,10 @@
      "output_type": "stream",
      "text": [
       "Eigenvalues:\n",
-      "[Obs[0.705(56)] Obs[4.39(20)]]\n",
+      "[Obs[0.705(57)] Obs[4.39(19)]]\n",
       "Eigenvectors:\n",
-      "[[Obs[-0.283(25)] Obs[-0.9592(74)]]\n",
-      " [Obs[-0.9592(74)] Obs[0.283(25)]]]\n"
+      "[[Obs[-0.283(26)] Obs[-0.9592(75)]]\n",
+      " [Obs[-0.9592(75)] Obs[0.283(26)]]]\n"
      ]
     }
    ],
@@ -364,7 +363,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {